Complexity of Jackiw-Teitelboim gravity

Adam R Brown,Ying Zhao,Henry W Lin,Leonard Susskind,Lárus Thorlacius,Hrant Gharibyan

doi:10.1103/physrevd.99.046016

Abstract

The Jackiw-Teitelboim (JT) model arises from the dimensional reduction of charged black holes. Motivated by the holographic complexity conjecture, we calculate the late-time rate of change of action of a Wheeler-DeWitt patch in the JT theory. Surprisingly, the rate vanishes. This is puzzling because it contradicts both holographic expectations for the rate of complexification and also action calculations for charged black holes. We trace the discrepancy to an improper treatment of boundary terms when naively doing the dimensional reduction. Once the boundary term is corrected, we find exact agreement with expectations. We comment on the general lessons that this might hold for holographic complexity and beyond.

Highlights

The Jackiw-Teitelboim (JT) model of 1 þ 1-dimensional dilaton gravity [1,2] is useful for studying conjectures relating the geometry of black holes and scrambling in dual quantum systems
The Jackiw-Teitelboim (JT) model arises from the dimensional reduction of charged black holes
Following our recent work [15], we find it useful to divide the spacetime geometry outside a near-extremal black hole into the three regions shown in Fig. 1: (i) Closest to the outer horizon of the black hole is the Rindler region, rþ < r ≲ 2rþ − pproffiffipffiffieffiffiffirffiffiffi distance from the horizon, r−, Δρ

Summary

INTRODUCTION

The Jackiw-Teitelboim (JT) model of 1 þ 1-dimensional dilaton gravity [1,2] is useful for studying conjectures relating the geometry of black holes and scrambling in dual quantum systems This simple model holographically reproduces the nearly conformal dynamics [3] of the Sachdev-Ye-Kitaev (SYK) model [4,5] at low energies. III we write down the action of the JT model and describe its black hole solutions This serves to fix notation and set up a simple 1 þ 1-dimensional framework where explicit calculations can be carried out to test proposals for holographic complexity. In [7,8], the late-time rate of change of the action of a WDW patch for RN black holes was calculated to be dS dðtL þ rRÞ

JACKIW-TEITELBOIM MODEL

AdS2 geometry and JT black holes

JT black hole thermodynamics

JT GRAVITY FROM DIMENSIONAL REDUCTION

VIII. CONCLUSION