I’ve been busy with other things, but after taking a look today at various new things related to quantum gravity, I was struck by how much things have changed sociologically in that subject over the last few years. Back in the days of the “string wars”, debates about quantum gravity were fiercely polarized. Oversimplifying and caricaturing the situation a bit, the two sides of the quantum gravity debate were:

- Those interested in loop quantum gravity as well as other more exotic attempts to reformulate the problem of quantum gravity. These people just considered pure quantum gravity and devoted a lot of effort to analyzing the deep conceptual issues that arise. They sometimes considered highly speculative hypotheses, trying out abandoning the usual basic axioms, for instance replacing fundamental axioms of quantum mechanics. Lee Smolin was an influential figure, and the Perimeter Institute a major center for this research.
- String theorists, who argued that the appearance of spin-two massless mode in the quantized string spectrum showed that string theory was the only way to understand quantum gravity. They claimed that they had a single, very specific and highly technical mathematical structure to study, which obeyed the conventional quantum theory axioms. Their efforts were devoted to specific computations in this theory, and they seemed to regard the other side of the debate as woolly thinkers, caught up in meaningless ill-defined philosophical speculation. The KITP at Santa Barbara, led by David Gross and Joe Polchinski, was a major center for this side of the debate.

These days, things have changed. If you’re at Perimeter, prominent activities include:

- This week’s conference on a very technical issue in string theory, superstring perturbation theory.
- This month’s course of lectures on Explorations in String Theory.
- The next public lecture will feature Amanda Peet promoting string theory. Peet has been one of the more ferocious partisans of the string wars. The text advertising her public talk a few years back at the Center for Inquiry in Toronto warned attendees who might consider “parrotting of critical views by outsiders like Lee Smolin.”

On the other hand, it you’re in Santa Barbara these days, you might be participating in a KITP conference on Quantum Gravity Foundations. This is featuring very little about the technical issues in superstring theory being discussed at Perimeter, but a lot of discussion of deep conceptual issues in quantum gravity. There’s also a lot of willingness to throw out standard axioms of physics, maybe even quantum mechanics. They’re even letting Carlo Rovelli talk.

The sort of speculation going on at the KITP is featured on the cover of this month’s Scientific American, and this week Quanta magazine will be publishing a series of pieces on something related, the “ER=EPR” conjecture. There’s debate whether anyone really understands this and whether it is consistent with standard quantum mechanics. It also features a diagram that people call the “octopus” diagram. Back in the day it was Lee Smolin who was getting grief for an “octopus” diagram (see here), yet another way in which things have changed.

For a more balanced view of quantum gravity issues, you might want to spend your time in France, where the IHES recently hosted an interesting series of surveys of the subject (see here), and the Quantum Gravity in Paris conference featured more specialized talks. In the category of quantum gravity topics I wish I had more time to learn about, Kirill Krasnov’s talk was presumably related to this recent work, which looks intriguing.

S,

I moved your comment to here. That topic is very relevant to the general theme of the posting: 15 years ago this kind of attempt to explain quantum gravity as “information” would have been the kind of thing the string theory community would have little time for. Things have changed.

I don’t understand though exactly what these people are doing so won’t comment on it specifically. In general I’m skeptical about this sort of thing. There’s a long tradition of attempts to derive fundamental physics from simple-minded models of 0s and 1s, it’s a favorite idea of a wide range of people from crackpots to great scientists. As far as I can tell it has never gone anywhere, and the mathematical ideas that have been successful in fundamental physics are ones of a very different nature. On the other hand, an infinite dimensional Clifford algebra acting on qubits maybe is closer to fundamental physics.

One thing to note about the Ouellette Quanta article is that I don’t think she mentions that her husband has just been coauthor of a paper on the precise topic she is writing about, see

http://arxiv.org/abs/1504.06632

From my limited knowledge, my impression is that one fundamental limitation of AdS/CFT schemes seems to be the lack of an algebraic structure that can determine the “data” of the CFT. In 1+1-D CFT, the differential equations satisfied by correlation functions derive from specializing the generic Verma module to descendants of an appropriate primary field. At least for a rational CFT the spectrum is determined by the algebra. Of course the conformal group is finite in d > 2 and it’s not clear to me what if any connection one has between local QFTs and “central extensions” of higher dimensional loop algebras (analogs of Kac-Moody).

If the CFT is in some general sense “non-integrable,” then it makes sense that the crucial data (scaling dimensions, OPE coefficients) cannot be exactly computed via some machine, algebraic or holographic. But one might hope that correlation functions beyond the trivial ones (four point and higher) are determined, if one can input the necessary data obtained elsewhere (epsilon expansion, numerics…). Do we know if this is the case? From conversations I’ve had with experts, I have the impression that these correlators might be less universal than in 1+1-D CFT. Then one needs to understand how to classify different holographic duals. Naively I would expect that has something to do with the additional space used for compactification on the gravity side, which is usually not discussed in applications to condensed matter…

Matthew,

The higher-dimensional analogs of affine algebras can not arise in QFT. Gauge anomalies in Yang-Mills theory in 3+1D are proportional to the third Casimir, but the Kac-Moody extension is proportional to the second. Hence the multi-dimensional affine extension requires that we go beyond QFT.

As you noted, the conformal group is finite-dimensional when d \geq 3, but the Virasoro algebra also arises as an extension of the diffeomorphism algebra on the circle. As such it has a direct generalization to higher dimensions, but the extension is not central except when d=1.

At least in statistical physics there is strong reasons to expect universality to hold, both from experiments and from theoretical considerations (4-epsilon expansion).

@ Thomas Larsson,

Thanks–I’m not an expert on the anomaly structure in QCD so your comment is very helpful. But I wonder if there might be connections between affine algebras and non-gauge theories. A trivial observation is that you get a loop algebra as the commutation relations of spins on any lattice, when expressed in terms of momentum modes. Obviously that doesn’t help you understand anything about a particular Hamiltonian. But I wonder if non-trivial extensions can give rise to interesting representations that might “exactly solve” some the low-energy sector of some (artificial but non-trivial) quantum spin models. Locality would be the hard thing to achieve I would guess, but there are useful non-local spin models that arise as mean field approximations in condensed matter or in cavity QED type schemes.

Matthew, there is a large body of work on the questions you are raising, and this is probably not the best place for this discussion. Briefly, it is true that the higher dimensional CFTs in AdS/CFT are not integtable, but one perspective is that this is what makes them interesting. For example there is recent effort to quantify quantum chaos using this framework, for which genericity arguments are more powerful than algebraic structures. As you expect from a quantum chaotic system, for generic observables there isn’t a closed form expression, or a convergent series expansion. Another comment is that AdS/CFT is no longer a good name for the subject, since most of the work has to do with massive deformations of CFTs and other non-CFTs, so this is really duality relating continuum QFT to gravitational theories.

@ Moshe

Now I’m intrigued! Can you give a reference or two for the application to quantum chaos?

Best,

matt

Look at recent papers by Douglas Stanford and Steve Shenker, especially a very recent one with Juan Maldacena. This is pretty technical and not completely digested yet, but hopefully some of it will be useful.

I should also mention that Alexi Kitaev has been working on very similar ideas. There are various talks on the Internet (one in KITP in their ongoing entanglement program), but none of it is published as far as I know.

Thanks Moshe!