Electric conductivity in non-Hermitian holography

TL;DR

This paper explores the phase structure and charge transport in a non-Hermitian PT-symmetric holographic model, revealing three distinct phases and analyzing their conductivity properties, with implications for complexified gauge theories.

Contribution

It introduces a non-Hermitian PT-symmetric deformation in holography, analyzing its phase diagram and conductivity, which is a novel extension of holographic models to non-Hermitian systems.

Findings

Identified three phases: stable PT-symmetric, unstable PT-symmetric, and PT-broken.

Confirmed the Ferrell-Glover-Tinkham sum rule in all phases.

Found a zero frequency spectral weight in a complexified U(1) rotor model.

Abstract

We study the phase structure and charge transport at finite temperature and chemical potential in the non-Hermitian PT-symmetric holographic model of arXiv:1912.06647. The non-Hermitian PT-symmetric deformation is realized by promoting the parameter of a global U(1) symmetry to a complex number. Depending on the strength of the deformation, we find three phases: stable PT-symmetric phase, unstable PT-symmetric phase, and an unstable PT-symmetry broken phase. In the three phases, the square of the condensate and also the spectral weight of the AC conductivity at zero frequency are, respectively, positive, negative, and complex. We check that the Ferrell-Glover-Tinkham sum rule for the AC conductivity holds in all the three phases. We also investigate a complexified U(1) rotor model with PT-symmetric deformation, derive its phase structure and condensation pattern, and find a zero frequency spectral weight analogous to the holographic model.