Lyapunov exponents in N=2 supersymmetric Jackiw-Teitelboim gravity

We study 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. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).

Automated summary

We study N = 2 supersymmetric Jackiw-Teitelboim (JT) gravity coupled to matter at finite temperature. The matter fields are related to superconformal primaries through AdS/CFT duality. Corrections to superconformal correlators arise due to broken super reparametrisation invariance in the SCFT dual. These corrections are generated by the exchange of super-Schwarzian modes, which dual to the exchange of 2D supergravity modes. We compute corrections to four-point functions of superconformal primaries and analyze the behavior of out-of-time-ordered correlators. The Lyapunov exponents of different components in the corresponding supermultiplet depend on whether the corrections are due to graviton, gravitini, or graviphoton exchange. If mutual two-point functions are non-zero, all components experience maximal Lyapunov exponent growth.