Holographic Non-Hermitian Lattices and Junctions and their RG Flows

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.

Comments: 42 pages, 24 figures. V2: corrected figures 3 and 7, added formula (3.19), minor typos corrected. V3: Published version. Includes major revisions. Corrects the analysis in Section 3.2, showing that PT is not broken. All related conclusions have been revised accordingly