## Friday, July 03, 2020

### Cumrun Vafa vs sloppiness of "lessons from JT gravity"

A decade ago, the main topic that clumped fundamental physicists to two camps was almost certainly the anthropic reasoning – or its flawed character. It gradually faded away because people agreed that there was no argument that would settle the question – and in the case of the anthropic approach, there wasn't a consistent theory that was ready to be used. Aside from some correct propositions that were worthless because they were tautological, the anthropic school was just an extreme ideology and it remained an extreme ideology.

Coleman's $$\alpha$$-parameters from baby universes were a prank or funny gesticulation, not a serious lecture about the actual mechanisms of quantum gravity.

But numerous other topics were fundamental enough and answered by highly controversial views. For example, late Joe Polchinski and his co-authors who are alive and kicking were promoting the idea that there was a firewall on the boundary of every black hole. It's obviously wrong and Joe was sort of accepting that it was wrong – but some people still enjoyed giving evidence to the answer that was wrong, the arguments were clever, and as long as you didn't throw away your common sense, you could have learned some things.

The JT gravity (plus the SYK model) is an ongoing minirevolution. JT is Jackiw-Teitelboim and it is a 2D gravity with a metric field and a dilaton$S = -\frac 12 {\rm d}^2 x \sqrt{g}\phi(R+2).$ where you are supposed to calculate the partition sums. One year or two years ago, it was even more fashionable to study the SYK model (Sachdev-Ye-Kitaee), a 0+1-dimensional model with $$N$$ fermions that are coupled to all others via a random quartic interaction. JT and SYK were often forced to interact with each other.

In March 2019, Saad+Shenker+Stanford (SSS) found a different way to calculate the JT partition functions: from a matrix model. There is an expansion in the matrix model and it may be interpreted as a contribution of world sheets with many disconnected components, each is attached to a D-brane. The SSS paper has over 100 citations by now.

The boundary representation of the partition sum may be interpreted as the averaging over many theories, something that Sidney Coleman did decades ago and that produced some evidence for "baby universes" in higher-dimensional gravity and their ability to yield new free $$\alpha$$-parameters in the theory of quantum gravity. Since my student years, I have been convinced – and later also encouraged by the PhD adviser Tom Banks to think – that the presence of these new parameters in quantum gravity is "breaking the general principles". Using the newer jargon, this kind of unlimited playing should belong to the swampland. You may have a bath in the mud (as a high school student during the potato picking brigade, I earned an extra \$1 by swimming in the swampland!) but you shouldn't walk through the university corridors in the landscape immediately afterwards!

I used the term "swampland" which was coined by Cumrun Vafa and some year or two ago, I didn't really follow (or study) what Vafa thought about these matters. But I would have bet that his views had to be very similar to mine and I think that I was totally right. In his April 2020 paper with Jacob McNamara, they enumerate many reasons why the JT fashion isn't relevant for our learning about quantum gravity in general (in spacetime dimensions $$d\geq 4$$ where quantum gravity becomes an impressive term).

So indeed, there seems to be a conflict between the things that the "JT fashion" people say about the JT model – something that they mindlessly extrapolate to all of quantum gravity; and Vafa's swampland restrictions. None of the two sides is rigorously established at this moment but if you ask me, there are much greater reasons to trust and extrapolate Vafa's swampland principles than to extrapolate some random mathematical property of a two-dimensional JT gravity model.

The second half of the abstract of Vafa-McNamara paper says (and Cumrun reiterated it in even more recent talks, see e.g. videos from February and May):
We further comment on the possible exceptions in $$d \leq 3$$ for this hypothesis and the role of an ensemble in holographic theories in the context of theories of quantum gravity in $$d=2$$ (such as JT gravity and possible cousins in $$d=3$$), which we argue are incomplete physical theories that should be viewed as branes in a higher dimensional theory of quantum gravity for which an ensemble plays no role.
OK, Vafa-McNamara's conclusion is surely the same as mine here. The JT ensemble-of-theories property is an artifact of this theory's having a low spacetime dimension. It is not a full-blown theory of "quantum gravity" that deserves this impressive name and that should pass nontrivial consistency checks. Instead, the "many ensembles" property of the theory really means that we're adding some contributions from many slightly random D-branes etc. in a broader theory. The broader theory is ignored by the treatment and this broader theory of quantum gravity wouldn't allow any ensemble interpretation and any free adjustable parameters.

On Page 2 (3 of 26 in the PDF), Vafa and McNamara list some of the common sense arguments why the widespread JT gravity manipulations with the partition sums don't represent an example of a proper calculation in a consistent and complete quantum gravity theory:
In the Euclidean path integral, spacetime wormholes can be interpreted as calculating amplitudes to produce or absorb baby universes. These processes pose a threat to unitarity of the quantum system, in the form of potential information loss [4, 5] or non-factorization of correlation functions in a holographic dual [8]. The proposed resolution is to suppose the baby universes are in a specific $$\alpha$$-eigenstate (in which case there are no issues with unitarity and factorization) at the cost of introducing α as free parameters of the theory, which are not the expectation value of any dynamical fields. Thus, we see an immediate tension between the Euclidean path integral and the expectation from the Swampland Program that quantum gravity should have no free parameters.
Exactly. A proper quantum gravity is a nontrivial mathematically formulated beast in theoretical physics that must pass many tests. Unitarity is clearly one of them and the Coleman baby universe games break the unitarity (or at least they generically threaten to do so); this is related to another breakdown, the breakdown of the factorization of the amplitudes. A proper theory of quantum gravity applies its power and consistency so that it bans any free parameters as well as global symmetries (these two are similar phenomena; in both cases, local scalar fields and local spin-one gauge fields are allowed as replacements for parameters or global symmetries). So these $$d=2$$ or $$d=3$$ theories of "quantum gravity" simply do not represent the kind of theories that we are getting in string theory, starting from $$d=10$$ or $$d=11$$, and that have so many incredible properties.

Vafa and his collaborator concluded – and I totally agree with the conclusion – that these JT games should be considered as a relatively uninteresting distraction in mathematical physics that applies to "something like a quantum theory of gravity but in $$d=2$$ or $$d=3$$" but whose lessons cannot be extrapolated to the full-blown theories of quantum gravity in $$d\geq 4$$. After all, Vafa often points out, there are very obvious reasons why the lessons from $$d=2$$ and $$d=3$$ should never be blindly interpreted as "lessons from quantum gravity". In particular, "quantum theories of gravity" in these low dimensions may have global symmetries, something that should be forbidden in the true quantum gravity in $$d\geq 4$$.

Violations of the unitarity or factorization conditions are problems that can be used as arguments against the "universalist extrapolations of JT gravity and the ensemble interpretation". However, I believe that just like your humble correspondent, Cumrun Vafa actually starts with something deeper, something that we consider more important, and it's the statement that a full-blown theory of "quantum gravity" is an extremely special theory that needs to pass some conditions – conditions such as the UV-IR relationships or modular invariance in perturbative string theory but possibly vastly extended – to prove that they are more than just some man-made mathematical masturbations. A genuine theory of quantum gravity passes an infinite number of consistency checks that a random man-made theory prepared to "emulate" quantum gravity doesn't respect.

And the JT gravity just doesn't have any such remarkable special traits. So it is an annoying propaganda to claim that the JT gravity is a theory on par with the $$d=11$$ M-theory, for example. This "equality" is absolutely disproportional because the JT gravity is just a cheaply constructed collection of man-made formulae while M-theory is a highly non-trivial pre-existing theory where everything fits together and that humans just discovered. (Maybe I should have used F-theory, a child of Vafa's, instead of M-theory because Witten, the father of M-theory, is apparently a member of the JT bandwagon.)

JT gravity isn't "wrong" or "low-brow" to the same extent as things like loop quantum gravity and similar pseudosciences marketed as "quantum gravity" but some "qualitative problems" with presenting these games as "research of universal properties of quantum gravity" seem very analogous in the JT and LQG cases. In both cases, the proponents really show that they have learned nothing about the stringy and string-like traits that a good theory of quantum gravity must possess. In this sense, they are as ignorant about the major issues as the first people who started to play with combinations of Einstein's general relativity and quantum mechanics in the first half of the 20th century (or when Coleman wrote his paper on the baby universes). They are a part of a community or tradition that has made no substantial progress for more than 50 years.

In other words, Cumrun Vafa is just protecting the godly brand of "stringy quantum gravity" against the insanely stupid and sort of insulting claims that "everyone and everything may be counted as stringy quantum gravity now, anyway". JT gravity is just some random collection of simple formulae that may be used as approximations of a complete theory of quantum gravity but it is not a complete theory of quantum gravity because it hasn't passed correspondingly difficult tests as e.g. M-theory in $$d=11$$. And in some proper counting, every theory of quantum gravity must pass the tests of the same total difficulty. The previous sentence is a belief of mine but I think that Vafa may share it and there are good reasons for this belief. In $$d=2$$ and $$d=3$$, the "number of structures and possible physical tests" is much lower which is why we should conclude that the question "whether JT is a proper theory of quantum gravity" to be either ill-defined or yielding a "No": the tests of QG-ness just cannot be successfully completed.

We had several discussions about this problem that "every theory is quantum gravity now" with Steve Shenker, among others. It is probably no coincidence that Shenker is one of the three S in the SSS paper on the ensemble interpretation of JT gravity. Already after the 1997-1998 discovery of AdS/CFT, Shenker concluded (although he wasn't happy about it) that now, every quantum field theory in $$d$$ dimensions may be interpreted as a quantum gravitational theory in $$d+1$$ dimensions via the AdS/CFT holographic dictionary. So the quantum theories of gravity were no longer precious, he thought: they were exactly as straightforward stuff as QFTs, he argued, simply because they were the same thing up to the shifted dimension.

I disagreed and I still disagree with this interpretation. What is actually precious and special about quantum gravity – and it is still precious and special now – is the ability of the amplitudes to get decompactified to a large enough (small curvature) spacetime with a high enough spacetime dimension, $$d\geq 4$$, where a complete unitary S-matrix exists at all energies and includes spin-two particles (or something in a curved background that may be shown to be as constrained as the flat space S-matrix). Most of the QFTs only produce highly curved AdS spaces so they're not the "rare and precious quantum gravity". On the other hand, the QFTs that produce nearly flat AdS spaces do yield AdS spaces "just with several" bulk theories in them (if you completely decompactify them). But vacua with flatter spacetimes and higher-dimensional spacetimes – "more geometric vacua" – are surely "more clear" examples of quantum gravity when they really work! The amount of evidence that "something is a proper theory of quantum gravity" may be tiny or zero for $$d=2$$ or $$d=3$$ theories such as JT.

Annoyingly enough, I feel that this new inclination to uncritically buy the statements that "any piece of mathematical notation resembling quantum mechanics and gravity is on par with quantum gravity and its general lessons may be extrapolated to all of quantum gravity" is correlated with the ongoing political and societal degeneration of the Western society under the influence of the SJWs. "Any mathematical masturbation is equal to M-theory" seems like another manifestation of the ideology that paints any kind of perversion as equally good as (and, in most cases, even much more equal than) some refined behavior that has passed the tests of decades or centuries.

It's of course dangerous – and never "completely exact" – to link people's opinions about physics and those about the society. But I do think that Vafa will understand me in this case and if he is labeled a heretic by the SJWs due to his opinions about the relevance of some manipulations in $$d\leq 3$$ for "general lessons in quantum gravity", he will embrace his important role of the anti-SJW-JT heretic with the maximum courage that history demands from him. Thank you, Cumrun. ;-)

P.S.: A new paper by Gliozzi argues that the 3D pure gravity is inconsistent today, using ST modular bootstrap arguments.