The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual

TL;DR

This paper explores the SYK model's soft mode, revealing a non-local correction to the Schwarzian action and connecting it to dilaton gravity, while also analyzing out-of-time-order correlators.

Contribution

It introduces a non-local correction to the Schwarzian effective action and links it to a gravity dual, providing new insights into the SYK model's low-energy behavior.

Findings

Identified a non-local correction to the Schwarzian action.

Derived the same effective action from a dilaton gravity perspective.

Discussed properties of out-of-time-order correlators in the model.

Abstract

We give an exposition of the SYK model with several new results. A non-local correction to the Schwarzian effective action is found. The same action is obtained by integrating out the bulk degrees of freedom in a certain variant of dilaton gravity. We also discuss general properties of out-of-time-order correlators.