Strongly Coupled 𝒫𝒯-Symmetric Models in Holography

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.

Keywords

• non-Hermitian physics
• PT symmetry
• gauge/gravity duality