nLab
Sachdev-Ye-Kitaev model

Contents

Context

Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

From Maldacena-Stanford 16:

Studies of holography have been hampered by the lack of a simple solvable model that can capture features of Einstein gravity. The simplest model, which is a single matrix quantum mechanics, does not appear to lead to black holes. 𝒩=4\mathcal{N} = 4 super Yang Mills at strong ’t Hooft coupling certainly leads to black holes, and exact results are known at large N for many anomalous dimensions and some vacuum correlation functions, but at finite temperature the theory is difficult to study.

A system that reproduces some of the dynamics of black holes should be interacting, but we might hope for a model with interactions that are simple enough that it is still reasonable solvable.

Kitaev has proposed to study a quantum mechanical model of NN Majorana fermions interacting with random interactions (Kitaev 15). It is a simple variant of a model introduced by Sachdev and Ye (Sachdev-Ye 93), which was first discussed in relation to holography in (Sachdev 10).

From Maldacena 18:

The SYK model gives us a glimpse into the interior of an extremal black hole… That’s the feature of SYK that I find most interesting… It is a feature this model has, that I think no other model has

References

General

Review includes

The model is due to

with further discussion in

Further developments in

  • Biao Lian, S. L. Sondhi, Zhenbin Yang, The chiral SYK model (arXiv:1906.03308)

See also

In AdS/CFT and string theory

Discussion in view of AdS-CFT duality, specifically AdS-CFT in condensed matter physics, includes:

Relation to black holes in string theory and random matrix theory:

Last revised on July 17, 2019 at 05:37:34. See the history of this page for a list of all contributions to it.