Black hole excited states from broken translations in Euclidean time

TL;DR

This paper investigates how breaking imaginary-time translation symmetry in Euclidean path integrals affects the relaxation of excited states in ${ m f N}=4$ SYM, revealing the emergence of causal shadows in the dual black hole geometry.

Contribution

It introduces a novel method to prepare excited states with broken translation symmetry using Euclidean path integrals and constructs corresponding mixed-signature black holes in AdS.

Findings

Broken imaginary-time translations lead to causal shadows in black hole geometries.

Path-integral states with broken symmetry are associated with deformed cigar geometries.

The study demonstrates the relaxation process of excited states to thermal equilibrium.

Abstract

We prepare an excited finite temperature state in ${\cal N}=4$ SYM by means of a Euclidean path integral with a relevant deformation. The deformation explicitly breaks imaginary-time translations along the thermal circle whilst preserving its periodicity. We then study how the state relaxes to thermal equilibrium in real time. Computations are performed using real-time AdS/CFT, by constructing novel mixed-signature black holes in numerical relativity corresponding to Schwinger-Keldysh boundary conditions. These correspond to deformed cigar geometries in the Euclidean, glued to a pair of dynamical spacetimes in the Lorentzian. The maximal extension of the Lorentzian black hole exhibits a `causal shadow', a bulk region which is spacelike separated from both boundaries. We show that causal shadows are generic in path-integral prepared states where imaginary-time translations along the thermal circle are broken.