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

## TL;DR

This paper analytically investigates the conformal SYK model, demonstrating that primary operator matrix elements align with the Eigenstate Thermalisation Hypothesis and exploring implications for AdS$_2$ gravity duals.

## Contribution

It introduces a version of the SYK model that maintains reparametrisation symmetry at all scales and analytically verifies ETH in this conformal setting.

## Key findings

- Matrix elements of primary operators conform to ETH predictions.
- The model preserves reparametrisation symmetry at all scales.
- Implications for states in AdS$_2$ gravity are discussed.

## 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 ${\cal O}_n$ of the CFT$_1$ take the form postulated by the Eigenstate Thermalisation Hypothesis. We also discuss the implications of these results for the states in AdS$_2$ gravity dual.