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Eigenstate thermalisation in the conformal Sachdev-Ye-Kitaev model: an analytic approach

  • Pranjal Nayak
  • Julian SonnerEmail author
  • Manuel Vielma
Open Access
Regular Article - Theoretical Physics

Abstract

The Sachdev-Ye-Kitaev (SYK) model provides an uncommon example of a chaotic theory that can be analysed analytically. In the deep infrared limit, the original model has an emergent conformal (reparametrisation) symmetry that is broken both spontaneously and explicitly. The explicit breaking of this symmetry comes about due to pseudo-Nambu-Goldstone modes that are not exact zero-modes of the model. In this paper, we study a version of the model which preserves the reparametrisation symmetry at all length scales. We study the heavy-light correlation functions of the operators in the conformal spectrum of the theory. The three point functions of such operators allow us to demonstrate that matrix elements of primaries \( \mathcal{O} \)n of the CFT1 take the form postulated by the Eigenstate Thermalisation Hypothesis. We also discuss the implications of these results for the states in AdS2 gravity dual.

Keywords

1/N Expansion AdS-CFT Correspondence Conformal Field Theory Field Theories in Lower Dimensions 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics & AstronomyUniversity of KentuckyLexingtonU.S.A.
  2. 2.Department of Theoretical PhysicsUniversity of GenevaGeneva 4Switzerland

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