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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">PT</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{PT} \)</EquationSource> </InlineEquation> 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.</p>

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Holographic non-Hermitian lattices and junctions and their RG flows

  • 期刊论文

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  • 发表日期：

    2025年7月29日

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  • Daniel Areán,
  • David Garcia-Fariña

摘要

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 \( \mathcal{PT} \) 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.