Lyapunov exponents in $\mathbf{{\cal N}=2}$ supersymmetric Jackiw-Teitelboim gravity

TL;DR

This paper investigates Lyapunov exponents in $ ext{AdS}_2$ supergravity with $ ext{N}=2$ supersymmetry, analyzing how different supergravity mode exchanges influence chaos and out-of-time-ordered correlators.

Contribution

It provides the first detailed analysis of Lyapunov exponents in $ ext{N}=2$ supersymmetric JT gravity, revealing mode-dependent chaos growth rates.

Findings

Different supergravity modes yield distinct Lyapunov exponents.

Maximal Lyapunov exponent occurs when two-point functions do not vanish.

Supermultiplet decomposition reveals mode-specific chaos behavior.

Abstract

We study $\mathcal{N}=2$ supersymmetric Jackiw-Teitelboim (JT) gravity at finite temperature coupled to matter. The matter fields are related to superconformal primaries by AdS/CFT duality. Due to broken super reparametrisation invariance in the SCFT dual, there are corrections to superconformal correlators. These are generated by the exchange of super-Schwarzian modes which is dual to the exchange of 2D supergravity modes. We compute corrections to four-point functions for superconformal primaries and analyse the behaviour of out-of-time-ordered correlators. In particular, four-point functions of two pairs of primaries with mutually vanishing two-point functions are considered. By decomposing the corresponding supermultiplet into its components, we find different Lyapunov exponents. The value of the Lyapunov exponents depends on whether the correction is due to graviton, gravitini or graviphoton exchange. If mutual two-point functions do not vanish all components grow with maximal Lyapunov exponent.