Equivalence of JT gravity and near-extremal black hole dynamics in higher derivative theory

Nabamita Banerjee,Muktajyoti Saha,Arnab Rudra,Taniya Mandal

doi:10.1007/jhep01(2022)124

Abstract

Two derivative Jackiw-Teitelboim (JT) gravity theory captures the near-horizon dynamics of higher dimensional near-extremal black holes, which is governed by a Schwarzian action at the boundary in the near-horizon region. The partition function corresponding to this boundary action correctly gives the statistical entropy of the near-extremal black hole. In this paper, we study the thermodynamics of spherically symmetric four-dimensional near-extremal black holes in presence of arbitrary perturbative four derivative corrections. We find that the near-horizon dynamics is again captured by a JT-like action with a particular namely R2 higher derivative modification. Effectively the theory is described by a boundary Schwarzian action which gets suitably modified due to the presence of the higher derivative interactions. Near-extremal entropy, free energy also get corrected accordingly.

Highlights

Since decades, one of the major goals of theoretical physics is to understand the quantization of gravity
Two derivative Jackiw-Teitelboim (JT) gravity theory captures the nearhorizon dynamics of higher dimensional near-extremal black holes, which is governed by a Schwarzian action at the boundary in the near-horizon region
We study the thermodynamics of spherically symmetric four-dimensional near-extremal black holes in presence of arbitrary perturbative four derivative corrections

Summary

Introduction

One of the major goals of theoretical physics is to understand the quantization of gravity. To understand the two dimensional gravitational dynamics, we need to non-minimally couple matter fields with gravity.2 One such model is Callan-Giddings-Harvey-Strominger (CGHS) model in asymptotically flat space [1], whereas another such model is Jackiw-Teitelboim (JT) [2, 3] theory, whose solution is asymptotically Anti de-Sitter(AdS) spacetime. In the low energy limit, JT appears as gravitational dual to Sachdev-Ye-Kitaev (SYK) model, a solvable 0 + 1 dimensional model of Majorana fermions with all possible random interactions [4,5,6,7,8,9].3 For both SYK and JT, the time reparameterization symmetry is explicitly broken at the boundary of the spacetime, and the effective low energy dynamics is described by a Schwarzian action [10, 11]. We shall be interested in the JT gravity model

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