Friday, February 05, 2021

JT supergravity and SYK described as type 0B strings

One of the themes that string theorists and string-like theorists recently spent time with is the JT (Jackiw-Teitelboim) supergravity. It's some gravitational theory in 2 spacetime dimensions. Well, there aren't too many gravitons and other things propagating in such a low spacetime dimension. But you may calculate \(Z(\beta)\), a partition sum.

I consider this theme a "microrevolution" because it doesn't quite reach the threshold of excitement for a minirevolution. This JT supergravity, a 2D dilaton gravity, has been linked to the Sachdev-Ye-Kitaev (SYK, random magnets) 1D quantum mechanical model which is pretty much a holographic description ("CFT") for this quantum gravitational theory.

OK, such "apparently non-stringy" quantum theories of gravity are always risky. The low spacetime dimension means that many of the methods and principles that operate in realistic quantum gravity in 4-11 spacetime dimensions may become invalid. Nevertheless, it is a highly justified position to assume that all truly consistent theories of quantum gravity should be a part of string/M-theory. Is that true for the JT supergravity?

Today, the answer "Yes" is advocated by Clifford Johnson, Felipe Rosso, and Andrew Svesko (USC/London) in the new paper
A JT supergravity as a double-cut matrix model.
Clifford Johnson wrote a blog post about this manuscript: Full Circle. The title was chosen because he has previously discussed a connection with type 0A string theory; now it is about 0B and by listing all letters between A and B, he has probably covered a "full circle" LOL. Of course, Johnson was unusually attracted to 0A at least since 2003.

They basically adapted a 2003 paper by Klebanov-Maldacena-Seiberg. Those authors have connected some unitary and complex matrix model theories to type 0 string theories. Note that type 0 (0A or 0B) string theories are close siblings of type II (IIA or IIB) string theories except that you only impose the "left-right shared" GSO projection which isn't enough to remove the tachyon from the spectrum. Also, the absence of the chiral GSO projections in type 0 string theories means that the whole spectrum is bosonic; there are no fermions like in type II string theories. (In some brane-bound Hilbert spaces, you may have fermions only instead.)

On top of that, to describe these low-brow, low-dimensional matrix models, the type 0 tachyonic string theories have to be combined with the linear dilaton, the Liouville stuff etc. In the fresh paper, Johnson et al. have to consider a double-scaling limit that zooms in and replaces some moving packets by double cuts. This limiting treatment of the matrix models gives them the power to claim that they are able to calculate observables precisely, non-perturbatively. And the matrix model may be considered as a combination of (infinitely many) minimal type 0 string theories. Well, I don't understand why one is allowed to "combine" physical theories, what is the physical meaning of such a generic hybrid.

Well, some fishy steps and simplifications – tachyons to start with, linear dilatons, double limits, and combinations of several models – are being made to connect these simplified models with string theory. One may discuss the "degree and character of fishiness" of these extra features (or pathologies) but I still believe that the total fishiness is nonzero and these theories can't be considered full-blown siblings of the truly consistent quantum gravity setups resulting from string theory, those that are needed to describe the world around us, too.

It's clearly a paper with some merit (and Johnson had some reasons to feel that "this might be right") but I find this whole refocus of the high-energy theoretical physics community on the low-dimensional models (below 4D spacetimes) extremely frustrating and disappointing. This is the kind of stuff that I have associated with the phrase "mathematical physics" which is dull and to be contrasted with the hot and cool "theoretical physics". To do something that tells us important things about the life, universe, and everything, you simply need to find something about physics in 4 dimensions and higher (where the graviton physical polarizations exist), not in 3 dimensions and lower! I wouldn't have ever joined the "mathematical physics" community and I think that the growth of that, and the suppression of proper brilliant theoretical physics, is ultimately driven by the ideologically driven decay of the society.

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