Non-Hermitian Holography
arXiv:1912.06647 · doi:10.21468/SciPostPhys.9.3.032
Abstract
Quantum theory can be formulated with certain non-Hermitian Hamiltonians. An anti-linear involution, denoted by PT, is a symmetry of such Hamiltonians. In the PT-symmetric regime the non-Hermitian Hamiltonian is related to a Hermitian one by a Hermitian similarity transformation. We extend the concept of non-Hermitian quantum theory to gauge-gravity duality. Non-Hermiticity is introduced via boundary conditions in asymptotically AdS spacetimes. At zero temperature the PT phase transition is identified as the point at which the solutions cease to be real. Surprisingly for solutions containing black holes real solutions can be found well outside the quasi-Hermitian regime. These backgrounds are however unstable to fluctuations which establishes the persistence of the holographic dual of the PT phase transition at finite temperature.
arXiv comment5 pages, 3 figures, v2: 5 figures, matches published version
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- Spontaneous Non-Hermiticity in Nambu-Jona-Lasinio model
- Non-Hermitian quantum system generated from two coupled Sachdev-Ye-Kitaev models
- Towards holographic flat bands
- Non-Hermitian BCS-BEC crossover of Dirac fermions
- The phase diagram and vortex properties of PT-symmetric non-Hermitian two-component superfluid
- symmetry-protected exceptional cones and analogue Hawking radiation
- Excitation Transmission through a non-Hermitian traversable wormhole
- Electric conductivity in non-Hermitian holography
- Non-Hermitian Quantum Quenches in Holography
- Operator size growth in Lindbladian SYK