Non-Hermitian Quantum Quenches in Holography

TL;DR

This paper explores the dynamics of non-Hermitian holographic field theories in the context of gauge/gravity duality, revealing how non-unitary evolution relates to violations of energy conditions and black hole horizon behavior.

Contribution

It demonstrates the connection between non-Hermitian couplings, energy condition violations, and horizon dynamics, and shows how non-Hermitian gauge fields can restore unitarity in holographic models.

Findings

Non-unitary evolution corresponds to NEC violation in the bulk.

Varying non-Hermitian couplings shrinks the black hole horizon.

Introducing non-Hermitian gauge fields can restore unitarity.

Abstract

The notion of non-Hermitian PT symmetric quantum theory has recently been generalized to the gauge/gravity duality. We study the evolution of such non-Hermitian holographic field theories when the couplings are varied with time with particular emphasis on the question non-unitary time vs. unitary time evolution. We show that a non-unitary time evolution in the dual quantum theory corresponds to a violation of the Null Energy Condition (NEC) in the bulk of the asymptotically AdS spacetime. We find that upon varying the non-Hermitian coupling the horizon of a bulk AdS black hole shrinks. On the other hand varying the Hermitian coupling in the presence of a constant non-Hermitian coupling still violates the NEC but results in a growing horizon. We also show that by introducing a non-Hermitian gauge field the time evolution can be made unitary, e.g. the NEC in the bulk is obeyed, and an exactly equivalent purely Hermitian description can be given.