### 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 (**O**ne dimensional **S**igma **M**odel of **E**verything ;-), 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
## 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 HAMILTONIANSInvestigations motivated by the loop space perspective on Type II superstring dynamics lead to insights concerning generaldeformations of two dimensional superconformal field theoriesas well as to a method forcovariant perturbative calculations of superstring spectraon general backgrounds with applications to strings inRR backgroundsandtest of AdS/CFT.Content:

1) What is

well known2) What is

not so well known3) What is

new4) What is

not fully understoodyet——————————————–

1) WHAT IS WELL KNOWN

——————————————–

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

What

deformationof the supercharges willpreservethis algebra?Witten (1982): Use polar form $d=(-i{Q}_{1}+{Q}_{2})$.

$\Rightarrow $ algebra isomorphism must preserve

nilpotencyof $d$ as well asadjointnessrelations:- - - - scalar $W$ induces a

potential(-> Morse theory)- - - - 2-form W induces

torsion(Froehlich et al.)- - - - $\Rightarrow $ deformation operator $W$ induces

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

- - - - now $\{Q,Q\}=H\pm i{\mathcal{L}}_{k}$

- - - - ${\mathcal{L}}_{k}=\{d,k\rightharpoondown \}$ 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${\mathcal{L}}_{k}$ now!$\Rightarrow [{\mathcal{L}}_{k},W]=0$

- - - - Super Virasoro algebra of the

superstring is of the above form!:The Killing vector

is the reparameterization Killing vector on loop space.

$\Rightarrow $

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 operatorin (-1,-1) picture (pre-image under T_F, \bar T_F)- - - - anti-hermitean part gives background

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

with $[{\mathcal{L}}_{v},W]=0$

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

$\Rightarrow $ covariant Hamiltonian ${H}_{v}$ for ALL (stationary) backgrounds which

computes string spectrum:- - - - application to

perturbative calculations of string spectrae.g. ${\mathrm{AdS}}_{3}\times {S}^{3}\to $pp-wave (hep-th/0311064)

- - - - some computational aspects are

simpler, some are more involved than in LCQ - butmore generally applicablethan LCQ- - - —————————————–

4) WHAT IS NOT FULLY UNDRESTOOD YET

- - - —————————————–

- - - - how to deal with

normal orderingbeyond first order??$\Rightarrow $

background equationsof motion beyond first order??- - - -

RR backgrounds?? (cf. hep-th/0205219)$\Rightarrow $ this would allow above perturbation technique in particular for

AdS/CFTon ${\mathrm{AdS}}_{5}\times {\mathrm{S}}^{5}$- - - - finally: deformation technique makes conenction to NCG manifest,

‘spectral string’(www-stud.uni-essen.de/~sb0264/p4a.pdf) (cf. Chamseddine, Froehlich)