## March 13, 2004

### DPG Symposium 2004

#### Posted by urs

I am on my way to the spring conference of the German Physical Society, the

Frühjahrstagung der Deutschen Physikalischen Gesellschaft

(in Ulm) where I am going to give a little talk on the stuff that I have been working on lately. Since everybody can simply announce participant talks at this conference this is not a big deal and I regard it as a warmup for later. This is maybe also the reason why many groups in Germany, notably in string theory, seem to ignore this conference altogether.

On the other hand, H. Nicolai will be there and talk about the cosmological billards that he has been working on together with T. Damour, M. Henneaux and others. As far as I understand they have the mind-boggling claim that by symmetry reducing generic supergravity actions to cosmological models and identifying the symmetry of the resulting mini-superspace (which generically leads to chaotic billard dynamics) one can guess a vast extension of this symmetry group and hence the mini-superspace-like propagation on this group, which is not mini at all anymore but a 1d nonlinear sigma model on this monstrous group, and that this is equivalent to full supergravity with all modes included!

Since this is done for the bososnic part of the action only, I once asked H. Nicolai if we couldn’t simply get the same for full supergravity by simply SUSYing the resulting 1d sigma model. Susy 1d sigma models are extremely well understood. We know that the number of supersymmetries corresponds to the number of complex structures on the target space and the supercharges are essentially the Dolbeault exterior derivatives with respect to these complex structures. Nicolai told me that I am not fully appreciating the complxity of this task, which may be right :-) Still, this sounds promising to my simple mind.

Reducing quantum gravity to a 1 dimensiuonal QM theory of course smells like BFSS Matrix Theory. I think I also asked Nicolai if he sees a connection here, and if I recall correctly the answer was again that things are more difficult than my question seemed to imply. :-)

On the other hand, sometimes simple-minded insights lead to the right ideas. In retrospect I am delighted that I had come across and discussed the form-field potentials on mini-superspace which generically give rise to the billiard walls and the chaotic dynamics discussed by Nicolai and Damour in my diploma thesis on supersymmetric quantum cosmology (see section 5.2).

In fact, the way that I treat supergravity in that thesis is precisely how I am imagining Nicolai et al. could try to susy their OSOE (One dimensional Sigma Model of Everything ;-), namely first symmetry reduce the bosonic theory and then susy the result (instead of symmetry reducing the susy theory as usual). Maybe this is crazy, maybe not…

Ok, who else will bet there? There are many LQG people. A. Ashtekar will give a general talk on LQG for non-specialist. Bojowald of course will talk about what is called ‘Loop Quantum Cosmology’. With a little luck I find an LQGist willing to discuss the LQG-string’ with me.

I would also like to talk to K.-H. Reheren, who has announced a talk on algebraic boundary CFT, about Pohlmeyer invariants, but I am not sure if he considers it worthwhile talking to me… :-/

There will probably (hopefully!) be many more intersting talks and people. If so, I’ll let you know…

P.S. Maybe I should mention that on occasion of the 125th birthday of Albert Einstein the entire conference is devoted to this guy. I am looking forward to hearing Clifford Will ask “Was Einstein right?”.

(Update 03/24/04)

Here are some pictures from Ulm and the conference:

Einstein was omnipresent on his 125th birthday in his native town:

Parts of Ulm University have a very interesting architecture:

Ashtekar talks about the limitations of string theory:

C. Fleischhack discusses the step in LQG the analogue of which for the ‘LQG string’ is considered problematic by some people.

My talk on deformations of superconformal field theories:

Posted at March 13, 2004 5:01 PM UTC

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### Sunday

It’s Sunday morning, I have had a little stroll through Ulm (‘in Ulm und um Ulm herum’ ;-). Einstein everywhere: The theater features a play about him, there are Einstein exhibitions, the bookstores have books about Einstein and relativity in their showcases, his face is there when you enter hotel lobbies.

C. N. Yang will give an ‘Einstein Lecture’ today, at Ulm University, but not before 19:30, so I have still some time to kill.

Of course I am working on my talk, which is due on Tuesday. Here is an outline of what I am going to say in that talk:

——————————————– ——————————————–

SUPERSTRINGS FROM LOOP SPACE PERSPECTIVE

$\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}$(DEFORMATION OF SCFTs AND COVARIANT HAMILTONIANS)

Investigations motivated by the loop space perspective on Type II superstring dynamics lead to insights concerning general deformations of two dimensional superconformal field theories as well as to a method for covariant perturbative calculations of superstring spectra on general backgrounds with applications to strings in RR backgrounds and test of AdS/CFT.

Content:

1) What is well known

2) What is not so well known

3) What is new

4) What is not fully understood yet

——————————————–

1) WHAT IS WELL KNOWN

——————————————–

- - - - consider an $N=2$, $D=1$ susy QM with supercharges ${Q}_{1}$, ${Q}_{2}$ and algebra$\left\{{Q}_{i},{Q}_{j}\right\}=2{\delta }_{\mathrm{ij}}H$

What deformation of the supercharges will preserve this algebra?

Witten (1982): Use polar form $d=\left(-i{Q}_{1}+{Q}_{2}\right)$.

$⇒$ algebra isomorphism must preserve nilpotency of $d$ as well as adjointness relations:

(1)$d\to {e}^{-W}d{e}^{W}$
(2)${d}^{†}\to {e}^{{W}^{†}}{d}^{†}{e}^{-{W}^{†}}$

- - - - scalar $W$ induces a potential (-> Morse theory)

- - - - 2-form W induces torsion (Froehlich et al.)

- - - - $⇒$ deformation operator $W$ induces background fields!

- - - - Generalization to global $N=1$, $D=2$ susy algebra: use a Killing vector $k$ and set

(3)${d}_{k}=d+\mathrm{ik}⇁$
(4)${d}_{k}^{†}={d}^{†}-\mathrm{ik}\wedge$

- - - - now $\left\{Q,Q\right\}=H±i{ℒ}_{k}$

- - - - ${ℒ}_{k}=\left\{d,k⇁\right\}$ is generator of translations along $k$!

——————————————–

2) WHAT IS NOT SO WELL KNOWN

——————————————–

Can this be generalized to local $N=1$, $D=2$ SUSY?

Yes! As above, but preserve nilpotency up to reparameterizations ${ℒ}_{k}$ now!

$⇒\left[{ℒ}_{k},W\right]=0$

- - - - Super Virasoro algebra of the superstring is of the above form!:

(5)${d}_{k}\sim \left(i{T}_{F}+{\overline{T}}_{F}\right)$
(6)${d}_{K}^{†}\sim \left(-i{T}_{F}+{\overline{T}}_{F}\right)$

The Killing vector

(7)${k}^{\left(\mu ,\sigma \right)}={X}^{\prime \mu }\left(\sigma \right)$

is the reparameterization Killing vector on loop space.

$⇒$ Superstring is Dirac-Kähler on loop space

- - - —————————————–

3) WHAT IS NEW

- - - —————————————–

a) superstring backgrounds from deformations (hep-th/0401175)

- - - - deformations of the above form give indeed all superstring backgrounds!

- - - - hermitean part of $W$ is background vertex operator in (-1,-1) picture (pre-image under T_F, \bar T_F)

- - - - anti-hermitean part gives background gauge transformations

- - - - reproduces ‘canonical deformations’ (hep-th/9902194) when truncated at first order - - - - well known example for gauge transformation: T-duality, (hep-th/9511061)

- - - - same possible for: S-duality (hep-th/0401175)

b) covariant Hamiltonians (hep-th/0311064)

- - - - deformation technique allows concise algebraic expressions for SCFT objects in arbitrary backgrounds

- - - - covariant Schrödinger equation for superstring:

(8)$4{ℒ}_{v}\mid \psi 〉=\left(\left[\left(d+{d}^{†}\right),v\wedge -v⇁\right]-\left[\left(d-{d}^{†}\right),v\wedge +v⇁\right]\right)\mid \psi 〉$

- - - - Generalizes to ALL of the above deformations by simply setting

(9)$v⇁\to {e}^{-W}v⇁{e}^{W}$
(10)$e\wedge \to {e}^{{W}^{†}}e\wedge {e}^{-{W}^{†}}$

with $\left[{ℒ}_{v},W\right]=0$

- - - - this is so far just a rewriting of the super Virasoro constraints but yields

$⇒$ covariant Hamiltonian ${H}_{v}$ for ALL (stationary) backgrounds which computes string spectrum:

(11)$E=〈{H}_{v}〉$

- - - - application to perturbative calculations of string spectra

(12)${E}^{\left(1\right)}=〈{H}_{v}^{\left(1\right)}〉$

e.g. ${\mathrm{AdS}}_{3}×{S}^{3}\to$pp-wave (hep-th/0311064)

- - - - some computational aspects are simpler, some are more involved than in LCQ - but more generally applicable than LCQ

- - - —————————————–

4) WHAT IS NOT FULLY UNDRESTOOD YET

- - - —————————————–

- - - - how to deal with normal ordering beyond first order??

$⇒$ background equations of motion beyond first order??

- - - - RR backgrounds?? (cf. hep-th/0205219)

$⇒$ this would allow above perturbation technique in particular for AdS/CFT on ${\mathrm{AdS}}_{5}×{\mathrm{S}}^{5}$

- - - - finally: deformation technique makes conenction to NCG manifest, ‘spectral string’ (www-stud.uni-essen.de/~sb0264/p4a.pdf) (cf. Chamseddine, Froehlich)

Posted by: Urs Schreiber on March 14, 2004 1:05 PM | Permalink | Reply to this

### Re: Sunday

Heard a very interesting and even moving, while unostentatious, talk by C. Yang about Albert Einstein, his ideas and his life.

Encountering Yang reminded me of the joke

Q: ‘Who invented the sledge hammer?’

A: ‘Mr. Sledge.’

It is almost like meeting somebody called ‘car’ or ‘lightbulb’, if you know what I mean. It’s kind of amazing.

Before the talk I met Rüdiger Vaas, who is science journalist for the german popular science journal Bild der Wissenschaft and is working a lot on reporting about research in quantum gravity. I had first met him at the Strings meet Loops symposium last year. His report on ‘Strings meet loops’ will appear in the next issue of BdW.

He tells me that more than half of the 12 pages long article will be concerned with LQG and in particular with M. Bojowald and his ‘Loop Quantum Cosmology’. Considering that also the recent issue of Scientific American had an article by Lee Smolin on LQG, which of course can be found translated in ‘Spektrum der Wissenschaft’, and considering that Spektrum and BdW are the two leading german journals for popular science, this gives an impressive amount of public attention for LQG here in Germany. Maybe there is a general tendency. The DPG Symposium here in Ulm is clearly dominated by LQG contributions. Kind of amazing when one is involved in the current discussion about the conceptual viability of LQG.

I mean, ok, it is not established that string theory will survive experimental tests and everybody is free to believe that it will not. But at least it is clearly about theoretical physics. All kinds of concepts in string theory will definitely survive in and enrichen theoretical physics even if it might turn out that gravitons are not excitations of some string.

But currently I am not so sure that LQG is even theoretically about physics.

But of course Bojowald’s claim to be able to connect quantum gravity with experimental MBR data is enchanting.

It would be great if for instance string cosmology could come up with a similarly nice cosmological model which removes and clarifies the initial singularity. Most of what I have heard so far about string cosmology was pretty disappointing. Veneziano’s pre-big bang model and similar scenarios always reminded me of the ‘then a miracle occurs’ mechanism. The interesting transition of the two classical branches remains a mystery.

Maybe Jacques Distler can increase my faith in string cosmology by reporting interesting results from the conference Cosmology and Strings that he mentions in his latest musings.

Posted by: Urs Schreiber on March 14, 2004 10:00 PM | Permalink | PGP Sig | Reply to this

### Re: Sunday

Hi Urs,

It just happens that the latest “Matters of Gravity” has an article you might find interesting.

The Quest for a Realistic Cosmology in the Landscape of String Theory
Andrew Chamblin

http://www.arxiv.org./abs/gr-qc/0403051

Eric

Posted by: Eric on March 16, 2004 1:35 AM | Permalink | Reply to this

### Re: Sunday

Many thanks for pointing me to this nice overview. Seems like there is still a very long way to go regarding questions like the fate of the BB singularity. But maybe something like the singularity resulution described in

S. Mathur, Where are the states of a black hole? (2004)

will one day also be found for the initial singularity.

Posted by: Urs Schreiber on March 16, 2004 7:50 PM | Permalink | PGP Sig | Reply to this

### Monday

This has been a very intensive day.

When I arrived (late) in A. Ahstekar’s talk this morning I had only five hours of sleep behind me, but I made it to the first coffee break without major casualties and resupplied myself with caffeine.

Ashtekar gave a general introductory lecture on LQG. Afterwards Peres talked about ‘Quantum Information and Relativity Theory’, being concerned with problems such as a quantum measurement in one frame may come before the measured event in another frame.

After the coffee break Clifford Will gave an extremely enjoyable talk on experimental tests of gravity. As I have said here, I learned that LISA will not be able to see primordial gravitational wave backgrounds due to the noise made by binary star systems in our galaxy.

After lunch the parallel sessions started. I had a problem, because I wanted to listen to the NCG stuff which was parallel to a session in which Folkert Müller-Hoissen gave a talk. Now, Eric and I have spent a lot of time with extending and generalizing the work by Dimakis and Müller-Hoissen and I had never met these authors before, so I decided to ditch the NCG session and sit in on ‘Symmetries, Integrability and Quantization’. It was sort of interesting, though I later learned that this way I missed a talk about NCG on Lorentzian spacetimes, which I really regret to have missed. I’ll need to talk to those people in private tomorrow.

Anyway, my hope was to get hold of Müller-Hoissen after the talks and get on his nerves by talking about discrete differential geometry. But unfortunately he was inolved in a discussion with somebody else about something else, which went on and on and on…

Finally I decided not to wait any longer and ran to the lecture auditorium to catch at least the second half of C. Fleischhack’s talk on ‘Progress and Pitfallls of LQG’. This was a very technical talk with lots of formulas with a huge amount of indices and symbol decorations. I have made a photograph of the point where he puts on the transparancy which says that now the spatial diffeomorphism constraints are solved. I believe that the field of LQG would maybe profit from deemphasizing technical details at this point and instead emphasizing the big crucial point: The diffeomorphism constraints are ‘solved’ without imposing Dirac constraint quantization.

I saw that Thomas Thiemann was in the audience, A. Ashtekar was, Hermann Nicolai was, and decided that it would be nice to continue our Coffee Table discussion about this point, which some people feel is a little problematic.

So as the talk was over I asked the lecturer about this point. He answered that this method is simpler than Dirac quantization and also has the advantge that also ‘large’ diffeomorphisms can be included, i.e. those that cannot continuously be connected to the identity (such as coordinate reflections).

When I began to argue that the method may be simpler but is not what Dirac tells us to do (for good reasons, like path integral and BRST formalism), A. Ashtekar approached me. He was very nice and helpful, as usual, and we went outside to further discuss things.

He checked if I am the one who had pointed him to the Coffee Table discussion and told me that he didn’t answer my email partly because he found some statements of the Coffee Table discussion overly offending. I think he is right about that and highly appreciate that he still very patiently talked and listened to me. Many thanks to Abhay Ashtekar, indeed.

First he said that the way LQG deals with the gauge constraints is not different from what one does in gauge theory. I replied that that has to do with the fact that the anomalies of the standard model happen to cancel, while it is not clear that those of canonical gravity would (without the ghost sector). I think he agreed.

I suggested that maybe LQG should then perhaps try to handle the ghost-extended Einstein-Hilbert action instead of the pure EH action. At least for 1+1 dimensional gravity this does indeed remove the anomaly, as is well known. I got the impression that A. Ashtekar found this idea is maybe worth considering (but I am not sure).

He told me that what he found problematic with the ‘LQG-string’ is that the method does not in any way seem to involve the fields on the background spacetime. I found this remark interesting, because it resonates with my own feelings concerning this point, which I have expressed here. A. Ashtekar hinted at some alternative approaches by himself and somebody else which are apparently under investigation, but I feel that I should not report on that here in public.

After this very illuminating discussion I was asked by somebody if I am working on LQG, because he had seen me pipe up in Fleischhack’s talk. After I had answered that to the negative we exchagned personal and scientific identities, and I was delighted to meet in Thorsten Prüstel somebody working on - guess what - discrete field theory on Lorentzian graphs.

We immediately had lots of things to talk about. I showed him Eric Forgy’s and mine pre-pre-print and he was very interested and invited me to give a talk about that at University of Hamburg. He himself is working on an interesting approach to get gravity from the nonunitary part of an extended gauge group on a graph field theory, roughly. I hope that when I am in Hamburg I will get the chance to learn more about that.

We already had to hurry to get to the ‘Welcome Party’. There we happened to sit next to Prof. Kastrup from Aachen. Kastrup was the thesis’ advisor of two of the leading figures in current LQG, namely Thomas Thiemann and Martin Bojowald. We learned how Thomas Thiemann as a student originally wanted to work on string theory and was later convinced to look into LQG.

I found it very interesting that Kastrup agreed with my assessment that LQG is not ‘canonical’ in the usual sense, because it does not represent the classical canonical coordinates and momenta as operators on a Hilbert space.

Indeed, in the afternoon I had heard the very interesting talk by Kastrup about quantization of integrable systems in angle/action variables. This is an interesting and subtle issue of canonical quantization, which can already be studied for the ordinary harmonic oscialltor.

The point is that by the naive correspondence rule one would think that, since the angle $\omega$ and the action $S$ are a pair of canonically conjugate coordinates and momenta (like the ordinary $q$ and $p$ are, too) there should be self-adjoint operators $\stackrel{̂}{\omega }$ and $\stackrel{̂}{S}$ which satisfy $\left[\stackrel{̂}{\omega },\stackrel{̂}{S}\right]=i$.

But it is easy to convince oneself that this cannot work, which has to do with the fact that the angle is defined only modulo $2\pi$, or, equivalently, that $\omega$ and $S$ do not provide global coordinates on phase space, because the origin has the usual coordinate singularity of polar coordinates in the plane.

Kastrup showed how with taking much care one can instead construct two other operators ${K}_{+}$ and ${K}_{-}$ such that together with ${K}_{0}=\stackrel{̂}{S}$ they give the Lie algebra of $\mathrm{SO}\left(1,2\right)$ and that from these the standard $\stackrel{̂}{q}$ and $\stackrel{̂}{p}$ can be reobtained. (This can be understood heuristically by thinking of the 2d phase space of the oscillator with the origin removed as a (‘light’-)cone.)

He concluded by saying that, while being equivalent to the quantization with $q$ and $p$, this could have experimental consequences in quantum optics. (I asked him about how this can be true, but unfortunately failed to understand his answer.)

Anyway, this is a nice example for how subtle ordinary canonical quantization itself can already be.

Posted by: Urs Schreiber on March 15, 2004 9:07 PM | Permalink | PGP Sig | Reply to this

### Tuesday

The talks today didn’t interest me much (things like ‘Einstein and art’) and I spent the time reading and answering my mail as well as preparing my own talk.

But I did have lots of very valuable conversations.

At lunch I met Hermann Nicolai and we had a long discussion about Pohlmeyer invariants, DDF invariants, LQG, the ‘LQG-string’, diffeomorphism anomalies in string theory, string field theory, Matrix Models and prejudices in quantum gravity.

To begin with, I was kind of surprised to learn that H. Nicolai, together with K. Peeters, is currently thinking about Pohlmeyer invariants himself. We discussed the known results regarding their quantization and I mentioned that I think that there is a solution to the apparent problems. H. Nicolai was interested and invited me to visit the AEI in April to talk about these ideas.

Then of course we discussed the ‘LQG-string’ and what can be learned from it about LQG itself. H. Nicolai said that he had hoped that the LQG people would find the anomaly for the string, which, as he said, he would have considered a breakthrough for the whole LQG field. But what has now actually been done, he said, reminded him more of certain artificial constructions in axiomatic field theory, which are also mathematically well defined but physically empty.

I asked him about what this now means for full LQG and he said that, similarly, he would expect that there should be an anomaly and that he finds the constructions done in LQG problematic.

I tried to understand how the same issue could be understood from within string theory, and he basically said that one would have to understand closed string field theory in order to tackle this question. But currently a satisfactory definition of closed string field theory is of course not known.

I said that I am wondering if we cannot learn anything in this regard from BFSS/IKKT Matrix Models. The authors of the IKKT/IIB model at least claimed that the permutation subgroup of the full $\mathrm{U}\left(N\to \infty \right)$ gauge group of the model becomes the diffeomorphism group in the limit. Heuristically, we can think of the matrices as describing discrete spacetime points and the permutation subgroup permutes these points, so is related to diffeos in some sense.

Hermann Nicolai didn’t know the details of this claim (me neither :-) and remarked that most permutations would give rather pathologic diffeos in the continuum limit. In any case, my uneducated guess is that the issue of diffeo anomalies and the like is hidden in the $N\to \infty$ limit of the matrix models, which is not well understood at all, as far as I know.

Since the time for the afternoon talk sessions was drawing near we stopped at this point. But as I was about to leave the cafeteria K.-H. Rehren approached me. I very much appreciated this, because from our previous online conversation I had gotten the, apparently wrong, impression that he wasn’t interested in my comments on Pohlmeyer invariants.

I was delighted that we immediately sat down, pulled out pens and paper and began doing algebraic calculations. I think that in a couple of minutes we could clarify issues that would have taken weeks by email, at the previous speed.

But then we really had to hurry, because I was the one supposed to give the next talk!

I am not sure if it is a good or a bad sign, but at this DPG spring conference of the faculties ‘Gravitation and Theory of Relativity’ and ‘Theoretical and Mathematical Foundations of Physics’ my talk is apparently the only one directly concerned with strings! But I couldn’t complain. With H. Nicolai, K.-H. Rehren and F. Müller-Hoissen in the audience I knew I was talking to people who I would have liked to ask about their opinion on my stuff at any rate.

Unfortunately, there wasn’t much time for questions and feedback. Let’s see what tomorrow brings… If nothing else, my talk will probably enter the annals of the DPG as the only one based on chalk and blackboard in the age of PowerPoint. ;-)

After the afternoon sessions I took care to catch one of the speakers on NCG whose talks I had missed the day before. I was lucky to get hold of a mathematical physicist of the name Paschke, who had given a talk on NCG on pseudo-Riemmanina manifolds. He had presented a technique where you slice a globally hyperbolic manifold in compact spatial leaves, perform ordinary NCG a la Connes on these spatial slices and then figure out how to glue the resulting spectral triples together to get a ‘spectral quadrupel’. At first it might seem that this way time is ‘commutative’ while only space is ‘noncommutative’, but the crux is apparently that it turns out that this is not the case and that in some sense also time becomes ‘noncommutative’. But I didn’t see this in any detail.

After having understood how Paschke is proposing to deal with NCG on pseudo-Riemannian spaces I tried to make him tell me what he thinks of Eric’s and mine approach which is supposed to deal, among other things, with pseudo-Riemannian discrete spaces.

Paschke emphasized that he finds it very problematic to break the compactness assumption of Connes’ approach, which technically means that one is (compact) or is not (non-compact) dealing with a ${C}^{*}$ algebra which has a unit, because then many of Connes’ theorems won’t hold if there is no unital ${C}^{*}$ algebra. That may be true, but I am under the strong impression that one can do interesting physics on non-compact noncommutative algebras nevertheless. But this will be a crucial point to be worked out if I want to communicate with the Connes school of NCG.

I have to run now to get to the debut performance (really, the official dress rehearsal) of Dirk D’ase’s ‘Einstein opera’.

Posted by: Urs Schreiber on March 16, 2004 6:36 PM | Permalink | PGP Sig | Reply to this

### Wednesday

Ulm is a nice little town at the feet of two mountains. One of these mountains carries the name ‘Einstein’ and enjoys sainthood. The other is called Eselsberg (‘donkey mountain’) and can actually be reached by mortals. On top of the Eselsberg there is the university and other scientific and industrial institutions, the total of which is called Wissenschaftsstadt (‘science city’).

There is a bus which takes me from my hotel in Ulm to this acropolis of science. Today I was late (again) for the first lecture. But I was lucky. K.-H. Rehren was late, too, and on the same bus.

He greeted me with the words that he had looked at my notes regarding Pohlmeyer invariants, which I had shown him the day before, and that he found some of the steps problematic. On our way to the lecture hall I tried to briefly sketch the resolution, but couldn’t quite convince him in terms of words.

During the first talks we both scribbled lots of algebra on scratch paper and as coffee break arrived we were able to agree that there is in fact no problem but that at one point notation and at another point an argument must and can be improved.

I very much enjoyed this constructive communication. While sipping our coffee we could even agree that the construction of classical DDF invariants for string does not have anything to do with fixing conformal worldsheet gauge, as opposed to what has been claimed recently.

That was great. K.-H. Rehren even demonstrated that the relation between Pohlmeyer invariants and DDF invariants holds on a larger part of phase space than I was originally able to show. There is only a subset of measure 0 on phase space where the equality between Pohlmeyer invariants and suitable polynomials of DDF invariants is technically problematic. (But I think by being careful we can even deal with that subset.)

After coffee break one of the highlights of the symposium was due, namely H. Nicolai’s talk on cosmological billards and the bold conjectures associated with them, which have been put forward by Damour, Henneaux and Nicolai, as I have mentioned before This is all very intriguing and maybe I’ll find the time to say more about it.

At lunch I was still discussing technical aspects of classical string invariants with Rehren, when Nicolai joined us and asked if we were making progress. I said that we made much progress in mutual understanding. Rehren still wants to go through the calculations again in private before signing my claims about Pohlmeyer invariants and DDF invariants, and I can only appreciate that.

Hermann Nicolai asked if this wouldn’t show that there must be things like critical dimension etc. in Pohlmeyer’s approach, too, whereas Pohlmeyer et al. argue that their approach works, if it works (so far a consistent quantization of the algebra of Pohlmeyer invariants has not been found), in any number of dimensions. But K.-H. Rehren pointed to the argument that he had presented before here at the String Coffee Table and according to which it is not clear yet if by relaxing some of the usual requirements on the reps of the Virasoro algebra one could avoid certain consequences.

When Rehren and Nicolai left for the afternoon talk sessions I noted that at the table next to me somebody was carrying a badge which indicated that his name was ‘Christoph Schiller’. I said: ‘Hey, I think I know you from the discussion forum sci.physics.research! You must be the one concerned with how general relativity has to do with a maximal force.’

And I was right. He briefly explained the idea to me, and it didn’t sound that crazy at all. It is essentially a modification of the old argument by Jacobson

T. Jacobson, Thermodynamics of spacetime: the Einstein equation of state (1995)

who showed that you can derive GR from certain assumptions about thermodynamics. Schiller apparently noted that at the beginning of Jacobson’s derivation one may replace the thermodynamic assumptions by the assumption that there is a maximum value of the force between any two extended bodies. Here it is important that these are not taken as pointlike. He says that when you put an extended test particle above the horizon of a black hole, the distance being equal to the test particle’s Schwarzschild radius, it will experience precisely that maximal force.

I haven’t checked any of this yet, but if right the software engineer Schiller may have added a curious observation to physics, which, he says, might be of value in teaching GR.

It is such a great weather outside that I’ll stop at this point and see if I can produce some endorphine by exposing my myself to the sunshine.

Posted by: Urs Schreiber on March 17, 2004 3:28 PM | Permalink | PGP Sig | Reply to this

### Re: Wednesday

The maximum force idea can be found explained either in the arxiv preprint physics/0309118 or on www.motionmountain.net
where it is worked into the general relativity section. (And for the record, I am a theoretical physicist, not a software engineer.)

Cheers
Christoph Schiller

Posted by: Christoph Schiller on April 19, 2004 9:09 PM | Permalink | Reply to this

### Re: DPG Symposium 2004

Hello all,

my article in the popular German science magazine “bild der wissenschaft” (April 2004 issue) about a conference “Strings Meet Loops” last year and further aspects which Urs has mentioned is now available also as an extended version in English (but without pictures and illustrations).

In the printed issue there is another article about loop quantum cosmology (not yet translated).

Perhaps you are interested.

Best, Rudy

http://www.arxiv.org/abs/physics/0403112
Title: The Duel: Strings versus Loops
Authors: Ruediger Vaas
Comments: Extended version from: Ruediger Vaas: Das Duell: Strings gegen Schleifen.
Published in: bild der wissenschaft (2004), no. 4, pp. 44-49.
- Translated by Martin Bojowald and Amitabha Sen. - 10 pages, including 1 table and references
Subj-class: Popular Physics
Journal-ref: bild der wissenschaft (2004), no. 4, pp. 44-49

Abstract:
Physicists in search of the foundation of the world: how tiny objects
can create matter, energy and even space and time - and possibly
into quantum geometry (loop quantum gravity) and string theory, written
report and review, based on the “Strings Meet Loops” conference at the
Max-Planck-Institute for Gravitational Physics (Albert Einstein Institute),
Golm/Germany, in October 2003. – Keywords: quantum geometry, loop quantum
gravity, string theory, string cosmology, spin networks, spin foams,
anthropic principle, theory of everything, Abhay Ashtekar, Martin Bojowald,
Michael Douglas, Jerzy Lewandowski, Hermann Nicolai, Robert Oeckl, Fernando
Quevedo, Carlo Rovelli, Amitabha Sen, Lee Smolin, Leonard Susskind.

Posted by: Ruediger Vaas on March 29, 2004 9:34 AM | Permalink | Reply to this

### Re: DPG Symposium 2004

Hi Rüdiger -

Thanks for the link! (By the way, did you see that over here somebody already tried to discuss your article?)

I see that the original title Strings meet loops was often (already at the conference) recalled as ‘strings versus loops’ and has now even become a duel! All hopes that strings and loops could be dual instead of dueling seems to have evaporated… ;-)

I found it interesting to read in your article, and was a little surprised, that (on p. 4) J. Lewandowsky and A. Ashtekar essentially argue that less people are working on LQG than on strings because the conceptual setup of LQG were somehow hard to understand for people trained in field theory. You cite Lewandowski as saying:

String theory has more appeal within the physics community because it uses the standard language of background dependent quantum field theory. Since it is compatible with other areas of theoretical physics, many people were able to make a continuous transition from particle physics to string theory. The framework of loop quantum gravity, on the other hand, is new and different from anything else. Therefore, one needs to invest a lot of time to develop a new intuition.

In my humble opinion it is dangerous to assume that string theorist don’t understand what background independence is and that this is the reason why they don’t endorse LQG. One motivation for ‘Strings meet Loops’ should have been to remove such misconceptions in mutual understanding.

In fact, after the talk by Jan Plefka on M-Theory, I was told by LQGist L. Freidel that he found the regulated supermembrane and the BFSS Matrix Model (which he had heard about in this talk) extremely exciting and that he is wondering why not more string theorists work on such non-perturbative formulations of the theory.

I think the answer to the latter question is ‘Because progress is difficult’. Therefore in the lunch break I tried hard to turn the tables and make Freidel interested in the IIB Matrix Model, which, I think, must be fascinating to everybody who likes the conceptual and philosophical basis of LQG. Indeed, I believe that in the context of the IIB Matrix Model concepts are being found which are much more radical in their background indepence than what is used in LQG. (See here for some references.)

Unfortunaley, when I said that one of the people working on Matrix Theory is Luboš Motl, Freidel seemed to lose interest in these theories, because he had seen the stromg criticism on LQG that Luboš had voiced on sci.physics.research.

My conclusion in that there is indeed a communication problem. But it is not due to string theorist not understanding the implications of background independence.

Posted by: Urs Schreiber on March 29, 2004 10:24 AM | Permalink | PGP Sig | Reply to this

### Re: DPG Symposium 2004

Hi Urs,

I don’t think that the string versus loop discussion is mainly a problem of (not) understanding background independence. If Jurek, Abhay and others are correct, it is rather a background dependence problem: namely what the scientific background the researcher has. Thus, among other (especially sociological) reasons it depends also on “philosophical” presuppositions, broadly speaking. And here general relativity and QFT differ of course.

But in the end, logical consistence, explanatory power, (perhaps) simplicity, and (especially) empirical adequacy including experimental tests will decide.

For the moment, a comparison of the goals and achievements of the contrahents (cf. the table at the end of my article) is quite interesting nevertheless. Evaluation, of course, is another story,

Best,
Rudy

Posted by: Rüdiger Vaas on March 29, 2004 10:56 AM | Permalink | Reply to this

### Re: DPG Symposium 2004

By the way, is that table inspired by the table in Smolin’s review? I recall that for instance the statement that the status of black hole entropy explanation is ‘partly’ in string theory and simply ‘yes’ in LQG raised quite some eyebrows.

Also, saying that ‘nature of matter’ in LQG is ‘spin network states’ is a curious claim. LQG does not achieve (nor attempt) any unification in this sense at all. See for instance Bojowald’s quantum cosmology: There the matter field is an extra field. It is by no means ‘part of the spin network’.

Did you talk with any string theorists about this table, for instance with H. Nicolai? What did they say?

Posted by: Urs Schreiber on March 29, 2004 11:10 AM | Permalink | PGP Sig | Reply to this

### Re: DPG Symposium 2004

Hermann Nicolai and Abhay Ashtekar got the table before publication and had nothing to complain.

The table was done by myself first. But, indeed, I consulted Lee Smolin’s useful review. Also I discussed every line of the table with Lee last February during a quantum theory conference in detail. But in the end the responsibility is up to me of course.

You wrote: “Also, saying that ‘nature of matter’ in LQG is ‘spin network states’ is a curious claim. LQG does not achieve (nor attempt) any unification in this sense at all.”

Agreed. What was meant was simply that matter - described with the ordinary standard model - is represented as spin network states. It is put in by hand and not explained. As I wrote: Here is a big advantage of string theory. In this respect, LQG has nothing to offer yet.

However, there is at least some kind of ontological reduction (or unification) not only in string theory but also in LQG. And this is remarkable and interesting - at least from a philosopher’s perspective.

Posted by: Rüdiger Vaas on March 29, 2004 11:45 AM | Permalink | Reply to this

### Re: DPG Symposium 2004

I am not sure in which sense there is ontological reduction or unification in LQG.

You write:

What was meant was simply that matter […] is represented as spin network states.

Hm, but a spin netweok state is just some particularly convenient element of the Hilbert space. It is no surprise that matter is described by states in a Hilbert space.

Will you be in Paris this summer at Strings 2004?

Posted by: Urs Schreiber on March 29, 2004 12:29 PM | Permalink | PGP Sig | Reply to this

### Re: DPG Symposium 2004

Regarding ontological reduction or unification: This is a feature which is eminently interesting not only in respect of fundamental physics.

A strong motivation since Presocratic times is to reduce the plurality of the phenomenal world to one (or a few) basic entities, principles, laws etc. From this perspective, string theory is very attractive. Psychologically speaking, such an Occamian attitude seems to be a main motivation in fundamental physics. Reduction and unification is both oeconomical and orientating.

While M theory hope to unify and reduce “stuff” and interactions, it still has spacetime as a stage. LGQ on the other hand treats all stuff and interactions alike and also spacetime. Everything is on the same footing, is feature of the same kind of entity. This goal is not reached yet (but perhaps it can be reached with SUSY etc.). On the other hand, string theorist’s hope is also to “build up” spacetime out of more fundamental entities, in the end.

Note that these questions are not (only) a matter of Hilbert space descriptions. They are about what is really out there… (But this is just informal talk - be careful not to be swamped in the infamous philosophical problems of the nature of reality, laws, math, subject independence etc…)

;-)

Posted by: Rüdiger Vaas on March 29, 2004 1:11 PM | Permalink | Reply to this

### Re: DPG Symposium 2004

Hi Rüdiger -

thanks for your nice reply. Yes, I agree that orou (‘ontological reduction or unification’ ;-) is important, because it is essentially nothing else than comprehension. If you have two seperate phenomena (e.g. gravity and gauge forces) you don’t know why they exist. As soon as you understand them as two aspects of the same underlying object (e.g. strings) you understand ‘why’ there are the original two phenomena. So a better understanding of the world will to some extend always be a search for orou. Agreed.

But unfortunately I still don’t quite agree with the statement that such a unification is obtained, or even attempted, in LQG.

LQG with matter is a framework where you pick some action functional of a spacetime theory, e.g. the action of Einstein-Yang-Mills theory, and apply a particular method to it to obtain something that could be called a ‘relaxed canonical quantization’ of the original theory.

The result is a theory where of course gravity and matter are both described with states in a single Hilbert space. But the analogue was already true for the classical theory that was ‘relaxed canonically quantized’: There both gravity and matter shared the same phase space of the entire theory.

This is not what is usually meant with ‘unification’. Unification should go along with some reduction of the information necessary to produce given phenomena. In string theory for instance therer is just the worldsheet action and from it alone follow all the fields on target space, including gravity, gauge fields, and matter. This may be physically right or not, but it is in any case a unification.

But in LQG we always have to start with the spacetime action functionals for all the fields that we want to have in the theory. There is no reduction of this information. If there were, we would get restrictions on the field content of the theory, as in string theory.

Posted by: Urs Schreiber on March 29, 2004 1:32 PM | Permalink | PGP Sig | Reply to this

### Re: DPG Symposium 2004

Hi Urs,

perhaps there was a misunderstanding. I never claimed (nor did LQGists) that there is a unification of forces or SUSY.

What I had in mind was a different kind of unification in quantum geometry which Jerzy Lewandowski described as (I quote him from my article): “All forces ‘live’ in similar ways within the spin network and are treated alike in quantum geometry, although they are not unified in the same sense as in string theory.”

This is a bold statement which should be discussed in more detail. (But I am not the expert.)

From a conceptual point of view it may be still bolder:

– If LQG is correct, a spin network (or spin foam) is all there is.
– If M theory is correct, strings AND spacetime is all there is.

Thus, M theory is less simple. This is just a cartoon, but you might see better what I have in mind.

Assume that some kind of SUSY (or SUGRA etc.) could be implemented in LQG. Then LQG would be ahead in terms of reduction and unification, wouldn’t it?

I fully agree with your interpretation of unification as comprehension. Also your other points should puzzle the LQGists.

Best,
Rudy

Posted by: Rüdiger Vaas on March 29, 2004 2:07 PM | Permalink | Reply to this

### Rigidity

Assume that some kind of SUSY (or SUGRA etc.) could be implemented in LQG. Then LQG would be ahead in terms of reduction and unification, wouldn’t it?

If it were true that you could couple any old (supersymmetric) field theory to (super)gravity and use LQG methods to quantize the theory (in other words, leaving aside all of the technical objections that have been discussed ad nauseum hereabouts), that would be a disaster for the theory.

There is no “decoupling limit,” in which quantum gravity effects are important, but other particle interactions can be neglected. Unless you know all particles and their interactions all the way up to the Planck scale, you cannot hope to extract any predictions from a theory of quantum gravity.

If you are free to tack on some arbitrary field theory with only massive degrees of freedom (at some scale well above observable energies, but below the Planck scale), then you lose any predictivity about quantum gravity effects.

Note that this is a very different problem than the one of vacuum-selection. Both theories might have many, many vacua, with different properties. But, figuring out which vacuum to expand about is a low-energy question, decidable, at least in principle, by low-energy observations.

What String Theory promises you is that the high-energy behaviour is universal, and hence that you can make reliable statements about quantum gravitational effects. (Whether you can measure such effects is another question. But the early universe, evaporating black holes, etc., are places where such effects would be important, and might lead to testable predictions.)

The inability to add arbitrary particles and interactions in String Theory has lead people to call it a “Theory of Everything”. This sounds like a bit of hubris. But it’s not. Any theory of quantum gravity that is not a “theory of everything” is, in fact, a theory of nothing.

Posted by: Jacques Distler on March 29, 2004 5:28 PM | Permalink | PGP Sig | Reply to this

### Re: DPG Symposium 2004

In addition to what Jacques said let me also point out another aspect. You wrote:

Assume that some kind of SUSY (or SUGRA etc.) could be implemented in LQG. Then LQG would be ahead in terms of reduction and unification, wouldn’t it?

I don’t think so.

First, it is not difficult to ‘implement’ susy in LQG. Just write down any susy action that you like and apply the ‘relaxed canonical quantization’ procedure of LQG. Since by construction this deals with everything (except the Hamiltonian constraint, which hasn’t been understood even for ordinary 1+3d gravity) it ‘works’ no matter what.

And it has in fact been written down:

Y. Ling & L. Smolin, Supersymmetric Spin Networks and Quantum Supergravity (1999)

But, as I said before, just writing down an arbitrary spacetime action and applying some quantization procedure to it is not at all a unification.

I am wondering where the idea comes from that just because ‘matter fields live on the spin network’, as I believe people say in LQG, implies any unification.

Indeed, I am wondering where the idea comes from, which is expressed by several LQGist quoted in your article, that LQG somehow predicts that space is a spin network.

After all, the spin networks are just peculiar basis elements of the Hilbert space of LQG. They are not physical, not even the knot states are. They still have to satisfy the Hamiltonian constraint. In general there is no reason to expect that the solutions to the Hamiltonian constraint (if the latter could be defined and if these solutions exist) are pure spin network states. Instead one would expect them to be (continuous) superpositions of many spin network states.

Therefore saying that ‘the universe […] is a gargantuan spin network’, as Smolin does in your article, is like saying a particle in a box is a plane wave. No it is not (necessarily). Instead, whatever it is it can be decomposed into plane waves.

It should be emphasized that spin networks are not something that the LQG formalism spits out after turning a crank. Spin networks are by no means ‘predictions’. Instead they are concepts used to write down the theory. Just like the harmonic oscillator is conveniently discussed in a basis of Hermite-polynom-like functions, the LQG formalism is conveniently formulated in terms of spin network states. But that’s just a choice of language. I could use any other basis if I wish.

So when you write:

If LQG is correct, a spin network (or spin foam) is all there is.

this is, in my opinion, not a correct description of the state of affairs. Apart from the fact that you need to introduce every single field (matter or force) into LQG by hand, there is no reason to expect that the state of the universe in LQG is a pure spin network state. Even if it were, it would need to be a state which explicitly (not implicily or automatically) determines the values of all other matter and force fields. These would not ‘follow’ from the spin network in any sense.

Hm, I keep talking about LQG. I would much rather talk about string theory!

Since you said

If M theory is correct, strings AND spacetime is all there is.

let me again make some advertizing for a different view:

It is debatable whether spacetime is a fundamental element of string theory. Even from the perspective of perturbative string theory this is not quite true, since all you really need is a consistent conformal worldsheet theory. In some cases you can interpret that as describing strings propagating in a smooth spacetime. But in some cases you cannot.

Let me quote Kris Kennaway:

Perturbative string theory is a world-sheet theory. This means that
we mostly care about 2-dimensional conformal field theory. We start
by writing down a CFT that is unitary and anomaly-free. Anomaly
freedom and unitarity constrains us to start with one of the 5 famous
classes of superstring theory (type I, IIA, IIB, 2 types of
Heterotic). We then have to make the total conformal anomaly of the
CFT vanish (by balancing off positive contributions from the
“internal” part of the CFT with the negative contributions from the
non-unitary ghost sector). If we do this by using a sigma model for
the internal CFT then this is the constraint that tells us that the
sigma model must have a 6-dimensional target space, giving 4+6=10
dimensions.

But no-one forces us to choose the CFT to be a sigma model. There are
lots of other choices of CFT with the right conformal anomaly that are
not sigma models.

[…]

In the worldsheet approach to string theory, the target space is a
derived quantity. If our CFT is a sigma model, then there are fields
living on the worldsheet that have a dual interpretation as
geometrical quantities of the target space. For example, the scalar
fields living on the worldsheet parametrise the embedding of the
worldsheet into the target space, so they are coordinates on the
target manifold. The worldsheet field with spacetime spin-2 gives you
the metric on the target space, and so on.

However, no-one forces you to make your CFT a sigma model. There are
lots of unitary CFTs with the right conformal anomaly to use them as
part of our worldsheet theory, but there is no sense in which they are
a sigma model.

For example, Gepner models have a finite number of primary fields, but
none of them make sense as coordinates parametrising the worldsheet
embedding into a target space. This is the sense in which there is no
6-dimensional target space geometry associated to the Gepner models.

This illustrates the point I made above: in string theory, space-time
is a derived quantity. It emerges as a consequence of two-dimensional
world-sheet dynamics, and it is not a static and unchanging background
of the theory. The topology - and even dimension - of this derived
target space may fluctuate and change drastically. Dimensions may
dynamically compactify and decompactify. Cycles of the manifold may
dynamically shrink and be replaced by other cycles of different
dimension. One Calabi-Yau manifold may dynamically turn into another
Calabi-Yau manifold (in fact it is believed that all Calabi-Yau
manifolds are smoothly connected in string theory by these processes).

But this is all fine, because these processes are smooth on the
worldsheet. Whenever the target space is behaving semi-classically,
its derived dynamics reduce to those of General Relativity. When the
target space becomes non-classical, then string theory produces
corrections to General Relativity in just the right way to smooth out
singular processes like topology change (also naked singularities,
etc), so everything is always smooth and non-singular from the point
of view of the string.

But one can do better than perturbative string theory in this respect. In non-perturbative formulations of string theory, like Matrix Theory or in AdS/CFT, the notion of spacetime is explicitly emergent. Apparently this hasn’t been popularized quite as much as the idea of spin networks have been, but see for instance transparacies 12 and 13 of this talk. The corresponding review paper is here and contains further references.

Posted by: Urs Schreiber on March 29, 2004 6:31 PM | Permalink | PGP Sig | Reply to this

### Re: DPG Symposium 2004

Hi Rüdiger -

I have tried to find more semi-popular accounts of the fact that spacetime is an emergent phenomenon in string theory.

Robert Helling was so kind to put a poster about his work on D-geometry on his website.

This is great stuff. If you have general or specific questions and/or want to see further literature please ask.

Posted by: Urs Schreiber on March 30, 2004 11:50 AM | Permalink | PGP Sig | Reply to this

### Re: DPG Symposium 2004

The above mentioned semi-popular article on loop quantum cosmology - i.e. Martin Bojowald et al.’s work about avoiding the big bang singularity - is now translated and available online.

Rüdiger Vaas: Der umgestülpte Urknall.
bild der wissenschaft, no. 4 (2004), pp. 50–55.
Translated by Amitabha Sen:
The Inverted Big-Bang
http://arxiv.org/abs/physics/0407071

Best wishes,
Rudy

Posted by: Rüdiger Vaas on July 21, 2004 8:29 PM | Permalink | Reply to this

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