Strongly Coupled PT-Symmetric Models in Holography

TL;DR

This paper explores holographic duals of strongly coupled PT-symmetric quantum field theories, analyzing their phase structures, non-Hermitian quenches, and lattices, revealing spontaneous PT-symmetry breaking and flows to PT-symmetric fixed points.

Contribution

It constructs holographic models for PT-symmetric theories, studies their phase diagrams, and investigates spacetime-dependent non-Hermitian couplings and their IR behavior.

Findings

Non-Hermitian lattices support imaginary currents and break PT-symmetry spontaneously.

These lattices flow to a PT-symmetric fixed point in the infrared.

Non-Hermitian quenches violate the null energy condition in the gravity dual.

Abstract

Non-Hermitian quantum field theories are a promising tool to study open quantum systems. These theories preserve unitarity if PT-symmetry is respected, and in that case an equivalent Hermitian description exists via the so-called Dyson map. Generically, PT-symmetric non-Hermitian theories can also feature phases where PT-symmetry is broken and unitarity is lost. We review the construction of holographic duals to strongly coupled PT-symmetric quantum field theories and the study of their phase diagram. We next focus on spacetime-dependent non-Hermitian couplings: non-Hermitian quenches and lattices. They violate the null energy condition in the gravity dual. The lattices realize phases supporting an imaginary current that breaks PT-symmetry spontaneously. Remarkably, these non-Hermitian lattices flow to a PT-symmetric fixed point in the IR.