The chiral SYK model in three-dimensional holography

TL;DR

This paper extends the holographic duality from the SYK model and 2D gravity to a 3D context, deriving a boundary action from chiral SYK models and connecting it to 3D gravity fluctuations, with applications to chaos.

Contribution

It introduces a higher-dimensional holographic correspondence using chiral SYK models and the Alekseev-Shatashvilli action, linking boundary dynamics to 3D gravity fluctuations.

Findings

Derived the Alekseev-Shatashvilli action from chiral SYK models.

Connected boundary effective action to fluctuations around Euclidean BTZ black holes.

Demonstrated maximal chaos in the chiral SYK chain and gravity dual.

Abstract

A celebrated realization of the holographic principle posits an approximate duality between the $(0+1)$-dimensional quantum mechanical SYK model and two-dimensional Jackiw-Teitelboim gravity, mediated by the Schwarzian action as an effective low energy theory common to both systems. We here propose a generalization of this correspondence to one dimension higher. Starting from different microscopic realizations of effectively chiral $(1+1)$-dimensional generalizations of the SYK model, we derive a reduction to the Alekseev-Shatashvilli (AS)-action, a minimal extension of the Schwarzian action which has been proposed as the effective boundary action of three-dimensional gravity. In the bulk, we show how the same action describes fluctuations around the Euclidean BTZ black hole configuration, the dominant stationary solution of three-dimensional gravity. These two constructions allow us to match bulk and boundary coupling constants, and to compute observables. Specifically, we apply semiclassical techniques inspired by condensed matter physics to the computation of out-of-time-order correlation functions (OTOCs), demonstrating maximal chaos in the chiral SYK chain and its gravity dual.