Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

April 17, 2011

Quantum Theory and Gravitation in Zurich

Posted by John Baez

There’s a conference on quantum gravity in Zurich this summer:

  • Quantum Theory and Gravitation, ETH Zurich, June 14–24, 2011. Local organizers: Jürg Fröhlich and Matthias Gaberdiel. Scientific advisory board: John Barrett, Harald Grosse, Hermann Nicolai, Roger Picken and Carlo Rovelli.

Speakers include:

  • Jan Ambjørn (Copenhagen)*
  • Joakim Arnlind (AEI Potsdam)
  • Abhay Ashtekar (Penn State)
  • Costas Bachas (ENS Paris)
  • John Baez (CQT / Riverside)
  • John Barrett (Nottingham)
  • Niklas Beisert (AEI Potsdam)
  • Matthias Blau (Bern)
  • Ali Chamseddine (Beirut)
  • Alain Connes (College de France, Paris)
  • Ben Craps (Bruxelles)
  • Axel de Goursac (Louvain)
  • Lance Dixon (SLAC)
  • Henriette Elvang (Michigan)
  • Klaus Fredenhagen (Hamburg)
  • Laurent Freidel (Perimeter)
  • Stefan Hollands (Cardiff)
  • Jens Hoppe (Stockholm)
  • Ted Jacobson (Maryland)
  • Jerzy Jurkiewicz (Krakow)
  • Gandalf Lechner (Vienna)
  • Jerzy Lewandowski (Warsaw)
  • Renate Loll (Utrecht)*
  • Roberto Longo (Rome)
  • Viatcheslav Mukhanov (Munich)
  • Hermann Nicolai (AEI Potsdam)
  • Martin Reuter (Mainz)
  • Carlo Rovelli (Marseille)
  • Misha Shaposhnikov (EPF Lausanne)
  • Raimar Wulkenhaar (Münster)

(* to be confirmed)

There will also be 2 or 3 further speakers on string theory, and further lectures by other participants.

I’ll give a talk on higher gauge theory, division algebras and superstrings. I’m looking forward to seeing many old colleagues and friends. Besides the people listed above, these include Harald Grosse, Roger Picken and my former students Jeffrey Morton (now working with Picken in Lisbon) and Derek Wise (now working in Erlangen).

After this conference I’ll go to Erlangen and talk to Derek until June 30th while my wife Lisa attends the annual meeting of a consortium on ‘Fate, Freedom and Prognostication: Strategies for Coping with the Future in East Asia and Europe’.

Then, fate willing, we’ll go back to Singapore. This is my big visit to the western world this year. So, if you’re anywhere near Zurich or Erlangen and you want to say hi, drop me a line.

Posted at April 17, 2011 10:38 AM UTC

TrackBack URL for this Entry:   http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2388

31 Comments & 0 Trackbacks

Re: Quantum Theory and Gravitation in Zurich

Will there be any talks or discussions that are open to a more general public?

Posted by: Tim van Beek on April 18, 2011 12:11 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

I imagine anyone who can stand to sit through them without causing trouble is welcome to attend!

Why, are you thinking of coming to a talk or two? Since I know you I can surely get you in, in the unlikely event that someone thinks you’re a dangerous crackpot.

Or are you hoping for some talks that are enjoyable by normal citizens? I don’t expect there will be any of those.

Posted by: John Baez on April 18, 2011 12:31 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

I’m thinking about it, from Munich, it is only a 4 hour ride by train to Zürich, straight through. But I won’t have time for two weeks - are people supposed to stay for all the time, or do you just pay the fee and choose the talks you’re attending for yourself?

Posted by: Tim van Beek on April 18, 2011 12:45 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

I don’t know if there’s a ‘fee’—that’s not nearly as common in theoretical physics as in subjects where people earn real money. The actual participants are mainly there by invitation, and they’re supposed to stay there most of the time, eat breakfast, lunch and dinner together, go on walks, etcetera — that’s how the real thinking gets done. But if you want to come for a little while and hear some talks, I bet that’s fine. Usually it’s local faculty members who do that.

I don’t know the rules, or if there even are rules, but that’s because in practice the audience for these things is severely limited by the difficulty in understanding what’s going on. In general, the only people who show up and get kicked out are crackpots who ask annoying questions.

I supposed you’d also get in trouble if you tried to get free food.

Posted by: John Baez on April 18, 2011 12:58 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

The registration form for the conference says that there is a 50 CHF fee for participants, but if it is okay not to register and pay, but to simply show up for one talk or two, I’ll wait for the abstracts of the talks and make up my mind later.

Some people may talk about topics I actually could try to understand. I’d also enjoy a refresher on this division algebra thing, of course :-)

Posted by: Tim van Beek on April 18, 2011 3:35 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

Since I’m not a conference organizer, and I’ve never been to the ETH before, I probably shouldn’t be advising you on these matters. But it would be great to see you, and it seems unlikely that they’ll get upset by someone who wants to hear a few talks.

If you decide to come, let me know when.

Posted by: John Baez on April 18, 2011 4:14 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

It may be a little bit premature to collect links to relevant material before there is a program and abstracts of the talks, but thanks to the internet I already had the opportunity to watch the talks at the AQFT - the first 50 years conference in Göttingen in 2009, including the ones by Klaus Fredenhagen, Stefan Hollands, Gandalf Lechner and Roberto Longo.

Maybe the organizers will group the talks thematically, so that the AQFT talks are scheduled on two or three consecutive days.

Posted by: Tim van Beek on April 19, 2011 7:58 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

There is a tentative schedule of talks now:

Tue 14.6.: Jacobson, Arnlind, Rovelli

Wed 15.6.: Blau, Ashtekar, Lewandowski, Ambjorn

Thu 16.6.: Baez, Beisert, [seminars by other participants]

Fri 17.6.: Bachas, Hollands, de Goursac, Mukhanov

Mon 20.6.: Dixon, Hoppe, Bossard, Lechner

Tue 21.6.: Longo, Elvang, Shaposhnikov, Barrett

Wed 22.6.: Craps, Reuter, Loll, Freidel

Thu 23.6.: Wulkenhaar, Reiterer, [seminars by other participants]

Fri 24.6.: Chamseddine, Nicolai

Posted by: John Baez on May 12, 2011 2:31 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

A detailed program of the conference can be seen here.

Because I’ll be jet-lagged at the beginning of the conference, they’re going to switch me and Carlo Rovelli, so I’ll be talking Thursday June 16th and he’ll be speaking Tuesday June 14th.

Posted by: John Baez on May 30, 2011 2:13 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

I’d be interested in hearing reports of any insights that Jens Hoppe might talk about, concerning his Fundamental structures of M(brane) theory , in his talk with the same title. (Just in case you or other nnCafé participants attending the conference feel like blogging about the talks a bit).

Posted by: Urs Schreiber on May 30, 2011 7:27 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

Thanks for pointing out that talk: I don’t know Jens Hoppe so I might not have known to pay attention. I doubt I’ll be heavily blogging about this conference, since I’m mainly eager to talk to a few people, but if I understand something about this talk I’ll let you know—probably right here.

Jeffrey Morton will be at the conference, and he likes to blog, so interested people should keep an eye on his blog. I don’t know any other bloggers who will be attending!

Posted by: John Baez on May 30, 2011 8:31 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

Interesting paper. Thank you for drawing attention to it. I’m especially intrigued by this quote:

“the Virasoro algebra being just the simplest example of certain (extended)infinite-dimensional diffeomorphism algebras”

I did not find the multi-dimensional Virasoro algebra in the text, but perhaps it is there implicitly.

Hm. I just noted that Jens Hoppe is at my alma mater.

Posted by: Thomas Larsson on May 30, 2011 8:42 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

I did not find the multi-dimensional Virasoro algebra in the text,

Equation (23). The structure constants are equation (26).

Posted by: Urs Schreiber on May 30, 2011 11:13 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

It seems like my excitement was premature. The paper never discusses any extension. More seriously, I fail to see how even the non-extended algebra can possibly be correct. To understand the construction, I specialized to the d-dimensional torus. The eigenfunctions in eqn (10) are then plane waves labelled by momenta α=m=(m i)\alpha = m = (m_i): Y m(ϕ)=exp(imϕ),Y_m(\phi) = \exp(im\cdot\phi), with Laplacian eigenvalues μ m=m 2=mm,\mu_m = m^2 = m\cdot m, and the dot product is contraction with the Minkowski metric. The structure constants in (26) become f mn r=(m 2n 2)mnm 2n 2δ m+n,r.f^r_{mn} = {{(m^2 - n^2) m\cdot n}\over{ m^2 n^2}} \delta_{m+n,r}. In 1D this is indeed the centerless Virasoro algebra (after a redefinition of the generators), but when d>1d \gt 1 it is wrong; the Jacobi identities fail. The problem has to do with the Minkowski metric. Constancy of the metric is not compatible with general diffeomorphisms, but only with the Poincare subalgebra. One could consider a flat metric which transforms under diffeomorphisms, but eqn (10) seems to contradict that; the Laplacian eigenvalues are treated as constants. Also note that none of the infinite-dimensional simple Lie algebras of vector fields (W, S, H, K series) have structure constants which involve a symmetric metric. Even if the algebra in this paper is not simple, it should have simple subalgebras. None of these can be infinite-dimensional if the Minkowski metric is in the structure constants.
Posted by: Thomas Larsson on May 31, 2011 5:43 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

the Jacobi identities fail

Right. Hm.

Posted by: Urs Schreiber on May 31, 2011 9:22 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

On the other hand, the Jacobi identity only needs to hold on the constraint surface (2).

But I’ll need to have a closer look at the computations. Not right now.

Posted by: Urs Schreiber on May 31, 2011 11:09 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

That certainly brings to mind BFV and/or BV constructions
If Jacobi fails for ghosts but holds on the constraint surface
then the ghosts for ghosts give Jacobi up to homotopy

Posted by: jim stasheff on May 31, 2011 1:40 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

That certainly brings to mind BFV and/or BV constructions

Absolutely. A more thorough discussion of the Nabu-Goto action functional in higher dimensions would proceed along these lines.

Posted by: Urs Schreiber on May 31, 2011 6:29 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

But on the constraint surface it is a proper Lie algebra, and as such subject to known classification theorems.

Posted by: Thomas Larsson on June 1, 2011 5:29 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

Both Ambjørn and Loll will be here, and presumably speak about their work on causal dynamical triangulations. Because this approach to quantum gravity discretizes slices up spacetime into surfaces of “constant time”, I’d always been worried that it was quantizing not general relativity but some other theory—one that has a built-in separation between time and space. Lately there’s been some new work delving into this question.

While general relativity with cosmological constant is singled out as the only theory with a diffeomorphism-invariant action built by integrating low-order derivatives of the metric, a splitting of spacetime into space and time lessens the symmetry of the theory and thus allows for more choices. Apparently all these choices are included in the theory called ‘Hořava-Lifshitz gravity’.

A new paper by Sotiriou, Visser and Weinfurtner suggests that causal dynamical triangulations could be a discretization of Hořava-Lifshitz gravity:

We explore the ultraviolet continuum regime of causal dynamical triangulations, as probed by the flow of the spectral dimension. We set up a framework in which one can find continuum theories that can fully reproduce the behaviour of the latter in this regime. In particular, we show that Hořava-Lifshitz gravity can mimic the flow of the spectral dimension in causal dynamical triangulations to high accuracy and over a wide range of scales. This seems to indicate that the two theories lie in the same universality class.

This paper reports on numerical work in 2+1 dimensions, not 3+1. But if causal dynamical triangulations is quantizing Hořava-Lifshitz gravity, that raises some big questions.

Posted by: John Baez on June 13, 2011 1:43 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

On the 14th Ted Jacobson kicked off the conference with a talk on the generalized 2nd law of thermodynamics, in which entropy increases if areas of ‘causal horizons’ are included as part of the definition of entropy. His student Aron Wall has written 3 papers on this subject, and his talk described this work:

The first paper critiques previous work. The second proves the generalized 2nd law in a semiclassical framework on a background spacetime that has both boost and null translation symmetries. The argument makes heavy use of the concept of relative entropy. The third paper generalizes the second one to a much wider class of spacetimes, assuming some axioms about the behavior of quantum fields on these spacetimes.

Posted by: John Baez on June 15, 2011 7:13 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

Thanks for posting notes on the talks here! That’s great.

I have taken the liberty of archiving your commented literature list in an nnLab entry generalized second law of thermodynamics .

Posted by: Urs Schreiber on June 15, 2011 11:18 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

Thanks! By the way, to show that entropy increases, a crucial step in Wall’s proof is to use the fact that the relative entropy obeys

S(ρ|σ)S(ρ|σ) S(\rho' | \sigma') \le S(\rho | \sigma)

where the states ρ\rho' and σ\sigma' are obtained by restricting the states ρ\rho and σ\sigma to a subalgebra of the original algebra of observables. I think Araki’s name comes up here.

Posted by: John Baez on June 15, 2011 1:22 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

Thanks, I have copied that information to the nnLab entry, too (no time to look into this myself right now).

I think Araki’s name comes up here.

That seems to be clear, as his definition of relative entropy for von Neumann algebra statesis needed to pass to the physically relevant case of non-finite probability spaces, I guess.

Posted by: Urs Schreiber on June 15, 2011 2:25 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

As Aron Wall notes himself in footnote 2 of the second paper, it is possible to prove that local algebras are of type III in quite general circumstances, so that there is no trace on local algebras.

Since a trace is necessary to define entropy, I’d guess that this line of thought cannot be relevant, i.e. one won’t be able to prove the generalized second law using the framework of AQFT on curved spacetimes.

Posted by: Tim van Beek on June 16, 2011 3:59 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

Hi everybody, I just stumbled upon this blog by chance .. and immediately found something interesting ;-)

Anyway, I just wanted to point out that absence of a trace does not necessarily imply that no meaningful concept of entropy exists. In fact, Araki defines his relative entropy between two states on a von Neumann algebra in terms of a relative modular operator, without making use of a trace. So there might be a chance of proving the generalized second law using operator algebras; that would be interesting indeed.

Posted by: Gandalf Lechner on June 16, 2011 5:39 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

Araki defines his relative entropy between two states on a von Neumann algebra in terms of a relative modular operator, without making use of a trace

Exactly. Definition and reference is recalled in the nnLab entry: relative entropy .

Posted by: Urs Schreiber on June 17, 2011 10:16 AM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

Tim wrote:

Since a trace is necessary to define entropy, I’d guess that this line of thought cannot be relevant, i.e. one won’t be able to prove the generalized second law using the framework of AQFT on curved spacetimes.

As Gandalf pointed out, you’re being overly pessimistic here. Relative entropy makes sense in some contexts (like type III factors) where ordinary ‘absolute’ entropy does not. I just thought I’d explain why, in simple vague terms.

Ordinary entropy tells you how disordered a state is. Relative entropy tells you how disordered one state is compared to another. The second one can be finite even in situations where the first is infinite.

Posted by: John Baez on June 23, 2011 12:07 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

Here are a few very sketchy notes on the conference. You can see talk slides here.

I think I’ll focus on the ideas of Jens Hoppe, since Urs was interested in his work.

First Joakim Arlind, a student of Hoppe, spoke about Poisson algebraic geometry and matrix regularizations. There’s a well-known ‘matrix regularization’ of membrane theory, developed by Hoppe and others, where you replace the algebra of functions on a Riemann surface by n×nn \times n matrices. In a suitable limit as nn \to \infty, we’re supposed to get the theory we really care about. The algebra of functions on a Riemann surface is a Poisson algebra thanks to its symplectic structure, and in the matrix regularization we replace multiplication of functions by matrix multiplication, Poisson brackets by commutators, and the integral of a function by the trace of a matrix.

I don’t think this plan ever succeeded in achieving what people want most of all, namely quantizing the supersymmetric 2-bane in 11 dimensions. There are some difficult issues of analysis involved in taking the limit, which are nicely summarized in this thesis:

The later parts of this thesis involve the spectra of Schrödinger operators, and any expert on those who wants to become famous should try to solve the open questions raised by membrane theory!

However, the idea has spawned a lot of interesting side-projects, one of which is the idea of generalizing ideas from geometry from manifolds to matrix algebra: a branch of noncommutative geometry. This is what Arlind’s talk was about.

Hoppe himself gave a blackboard talk, and unfortunately my notes only cover some fairly basic stuff. In a lunchtime conversation he did however explain to me how Poisson brackets are naturally replaced by Nambu brackets when we go to higher-dimensional membranes. I never really understood Nambu brackets in classical mechanics, so I was relieved to hear that Hoppe didn’t either. For him, it seems, Nambu brackets are only interesting when we start with a Riemannian manifold equipped with its volume form. For example, if we have a 3-manifold with volume form ω\omega, we can use the Riemannian metric to turn this into a trivector field with components ω ijk\omega^{i j k} and then define Nambu brackets by

{f,g,h}=ω ijk if jg kh \{f, g, h\} = \omega^{i j k} \partial_i f \partial_j g \partial_k h

The analogue of ‘matrix regularization’ in this case seems to remain obscure. One obvious guess is to use 3-index objects replacing matrices, but it’s still not obvious (at least to me, and perhaps to him either) how to generalize the matrix commutator in that case. He said he’d looked at Gelfand and Kapranov’s book on hyperdeterminants, without success.

He really liked my talk on Lie super-2-algebras, because he thinks we need to systematically boost up all concepts as we go from particles to strings to higher-dimenmsional membranes.

On a side note, Douglas Lundholm pointed out a certain Fierz identity which only holds in dimension 2, 3, 5 and 9. I think it appears on page 352 of his thesis, but also somewhere else in there. These dimensions are 1 less than the dimensions that superstrings and super-Yang-Mills theory enjoy most (3,4,6,10), I think because he’s doing light-cone quantization and suppressing one dimension. But as usual they’re related to the reals, complexes, quaternions and octonions.

He showed me a way to quickly check that this Fierz identity only holds in these dimensions, simply by summing over certain indices and showing this implies a relation between the dimension of the space of vectors and the dimension of the space of spinors. I’ve been a bit slow about checking that my favorite Fierz identities only hold in certain special dimensions. I didn’t think it could be this easy!

Posted by: John Baez on June 23, 2011 1:04 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

Hi John,

thanks for the summary of all this.

I could only glance over the references that you linked to. My very rough impression from these is that there has been less progress since back then on matrix membrane theory than I had been hoping for (but possibly I missed some highlights).

I am thinking: there are some indications that the next step after the sigma-model for the 1-brane (the string) to be usefully considered is possibly not so much the 2-brane (the membrane) but the 5-brane. Maybe I’ll find the time to make some blog post about this in the not too distant future.

Posted by: Urs Schreiber on June 27, 2011 7:23 PM | Permalink | Reply to this

Re: Quantum Theory and Gravitation in Zurich

People interested in the surprisingly good behavior of N=8N=8 supergravity in 4 dimensions might like the PDF files of talks by Guillaume Bossard and Henriette Elvang. There are some heroic calculations being done here!

Elvang’s talk gives a nice account of how the theory can be shown finite up to… 7 loops, it seems… using only symmetry arguments. Both SU(8)SU(8) symmetry and the hidden E 7(7)E_{7(7)} symmetry play a role here.

Posted by: John Baez on June 24, 2011 7:31 AM | Permalink | Reply to this

Post a New Comment