Holographic Non-Hermitian Lattices and Junctions and their RG Flows
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| Format: | Preprint |
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2024
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| _version_ | 1866911146278125568 |
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| author | Arean, Daniel Garcia-Fariña, David |
| author_facet | Arean, Daniel Garcia-Fariña, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13584 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holographic Non-Hermitian Lattices and Junctions and their RG Flows Arean, Daniel Garcia-Fariña, David High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology Quantum Physics 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. |
| title | Holographic Non-Hermitian Lattices and Junctions and their RG Flows |
| topic | High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology Quantum Physics |
| url | https://arxiv.org/abs/2410.13584 |