Non-Hermitian Holography

TL;DR

This paper explores the extension of non-Hermitian quantum theory to holography, analyzing PT symmetry, phase transitions, and stability of solutions in asymptotically AdS spacetimes with implications for gauge-gravity duality.

Contribution

It introduces non-Hermiticity via boundary conditions in holographic models and investigates PT phase transitions and stability of black hole solutions.

Findings

PT phase transition identified at zero temperature.

Real solutions exist outside the quasi-Hermitian regime.

Black hole solutions are unstable to fluctuations.

Abstract

Quantum theory can be formulated with certain non-Hermitian Hamiltonians. An anti-linear involution, denoted by PT, is a symmetry of such Hamiltonians. In the PT-symmetric regime the non-Hermitian Hamiltonian is related to a Hermitian one by a Hermitian similarity transformation. We extend the concept of non-Hermitian quantum theory to gauge-gravity duality. Non-Hermiticity is introduced via boundary conditions in asymptotically AdS spacetimes. At zero temperature the PT phase transition is identified as the point at which the solutions cease to be real. Surprisingly for solutions containing black holes real solutions can be found well outside the quasi-Hermitian regime. These backgrounds are however unstable to fluctuations which establishes the persistence of the holographic dual of the PT phase transition at finite temperature.