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arXiv · 2410.13584

Holographic Non-Hermitian Lattices and Junctions and their RG Flows

Daniel Arean·David Garcia-Fariña
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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.

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Daniel Arean, David Garcia-Fariña. 2024-10-17. Holographic Non-Hermitian Lattices and Junctions and their RG Flows. https://arxiv.org/abs/2410.13584

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