Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Why is SYK model important?

+ 6 like - 0 dislike
1191 views

In the past one or two years, there are a lot of papers about the SYK model, which I think is an example of $\mathrm{AdS}_2/\mathrm{CFT}_1$ correspondence. Why is this model important?

This post imported from StackExchange Physics at 2017-02-14 10:43 (UTC), posted by SE-user Chan
asked Dec 21, 2016 in Theoretical Physics by Chan (30 points) [ no revision ]

2 Answers

+ 6 like - 0 dislike

People hope that it may be an example of AdS/CFT correspondence that can be completely understood.

AdS/CFT correspondence itself has been an incredibly important idea in the hep-th community over the past almost twenty years. Yet it remains a conjecture. In the typical situation, quantities computed on one side of the duality are hard to check on the other. One is computing in a weakly coupled field theory to learn about some ill defined quantum gravity or string theory. Alternatively, one is computing in classical gravity to learn about some strongly interacting field theory where the standard tool box is not particularly useful.

The original hope was that SYK (which is effectively a quantum mechanical model) might have a classical dilaton-gravity dual description in an AdS$_2$ background. That hope seems to have faded among other reasons because the spectrum of operator dimensions does not seem to match. Yet, there still might be a "quantum gravity" dual, for example a string theory in AdS$_2$. String theories in certain special backgrounds have been straightforwardly analyzed.

This post imported from StackExchange Physics at 2017-02-14 10:44 (UTC), posted by SE-user user2309840
answered Dec 21, 2016 by user2309840 (60 points) [ no revision ]
+ 6 like - 0 dislike

SYK model provides us with the simplest example of holography which is much easier to study than canonical $AdS_5 \times S^5$ case due to much lower dimensionality. It was the initial motivation for Kitaev to study this model. Here is a set of 2 lectures in which he briefly discusses it.

Because of its simplicity, it is easy to consider the thermal and chaotic behavior of this theory and its gravity dual. Look at the following papers for the details:

Maldacena, Stanford "Comments on the Sachdev-Ye-Kitaev Model". It describes the correspondence in details.

Maldacena, Stanford, Yang "Conformal Symmetry and its Breaking in Two Dimensional Nearly Anti-de-Sitter Space". This paper describes the gravity side of the correspondence. In particular, modified gravity on the N(early)AdS space on which the bulk theory must live, because usual GR is trivial in 2D.

Shenker, Stanford "Stringy Effects in Scrambling". Here the stringy effects which must be taken into account in addition to field-theoretical gravity in the bulk are discussed.

This post imported from StackExchange Physics at 2017-02-14 10:44 (UTC), posted by SE-user Andrey Feldman
answered Dec 21, 2016 by Andrey Feldman (904 points) [ no revision ]
usual GR is trivial in 2D. First, is this (2+1)-D or (1+1)-D? Second, what does the statement exactly mean?

This post imported from StackExchange Physics at 2017-02-14 10:44 (UTC), posted by SE-user Abhinav
@Abhinav GR in 1+1 or 2D is trivial in the sense that $R_{\mu \nu}-\frac{1}{2} R g_{\mu \nu} \equiv 0$. In Euclidean signature the Einstein-Hilbert action is proportional to a topological quantity called Euler characteristics, so its infinitesimal variation is always zero.

This post imported from StackExchange Physics at 2017-02-14 10:44 (UTC), posted by SE-user Andrey Feldman

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysics$\varnothing$verflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...