The String Worldsheet as the Holographic Dual of SYK State

TL;DR

This paper proposes that the fluctuations of an open string in AdS space, exhibiting chaos and symmetry properties similar to the SYK model, can serve as a holographic dual to the SYK state, linking string theory and quantum chaos.

Contribution

It introduces a conjecture that the string worldsheet action in AdS space is a dual description of the SYK model, based on symmetry and chaos properties.

Findings

String fluctuations in charged BTZ black hole match SYK low-energy behavior

String worldsheet exhibits reparametrization symmetry akin to SYK

Euclidean IR fixed point governed by Schwarzian action

Abstract

Recent studies of the fluctuations of an open string in AdS space show some pieces of evidence that the string with a worldsheet horizon could be a dual description of SYK model, as they saturate universal chaos bound and share the same symmetry. An open string hangs from the AdS boundary to the horizon of black brane could be dual to a 0+1 dimensional boundary state. To be specific, we find that the fluctuation of the string in charged BTZ black hole has an asymptotic scaling symmetry, and its Euclidean IR fixed point is governed by the quadratic order of Schwarzian action, which is just the low energy effective theory of the SYK model. Considering the open string worldsheet also has natural reparametrization symmetry, we conjecture that the action of the string worldsheet is a dual description of SYK state.