Holographic Non-Hermitian Lattices and Junctions and their RG Flows

TL;DR

This paper explores inhomogeneous non-Hermitian holographic field theories, revealing complex RG flows and solutions with PT symmetry, some of which violate energy conditions near the boundary.

Contribution

It introduces models of non-Hermitian holographic lattices and junctions, analyzing their RG flows and PT symmetry properties, with novel solutions that challenge traditional energy conditions.

Findings

Non-Hermitian models can be mapped to Hermitian ones via complex gauge transformations.

Solutions with imaginary currents preserve PT symmetry and unitary evolution.

Some solutions violate the null energy condition near the boundary.

Abstract

We construct and study inhomogeneous non-Hermitian strongly coupled holographic field theories. We consider two models: a lattice where in each site there is some inflow/outflow of matter and a Hermitian/non-Hermitian/Hermitian junction. By tuning a complex external gauge field, we find a non-Hermitian model which can be mapped to a Hermitian one via a complexified U(1) gauge transformation. On the other hand, in the absence of the gauge field we find non-Hermitian solutions with a purely imaginary current. Despite this, all expectation values respect PT symmetry and thus we expect the system to feature unitary time evolution. Nonetheless, we have not found a map bringing these solutions to a Hermitian description. We study the RG flows of solutions with imaginary current finding that in the IR they can be mapped to a Hermitian conformal fixed point via a complexified U(1) transformation. Remarkably, we also obtain solutions where the null energy condition is violated near the boundary of the dual geometry.