Holographic Non-Hermitian Lattices and Junctions with $\mathcal{PT}$-Restoring RG Flows

We construct and study inhomogenoeus 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. In both cases, depending on whether we turn on a complex external gauge field, we find solutions that spontaneously break $\mathcal{PT}$ (thus hinting at a lack of unitary evolution) and solutions that do not. The former present an imaginary current responsible for the spontaneous breaking of $\mathcal{PT}$. We also study the IR geometry of these solutions finding that they flow to a $\mathcal{PT}$-unbroken fixed point. This leads us to claim that there is a $\mathcal{PT}$-symmetry restoration in the IR, similar to the one observed in the perturbative setup of [2110.05289].