Non-hermitian holography

Arean, Daniel; Landsteiner, Karl; Salazar Landea, Ignacio

doi:10.21468/SciPostPhys.9.3.032

SciPost Physics

Non-hermitian holography

Daniel Areán, Karl Landsteiner, Ignacio Salazar Landea

SciPost Phys. 9, 032 (2020) · published 3 September 2020

doi: 10.21468/SciPostPhys.9.3.032
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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 at finite temperature real black holes 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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.9.3.032
TI  - Non-hermitian holography
PY  - 2020/09/03
UR  - https://www.scipost.org/SciPostPhys.9.3.032
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 9
IS  - 3
SP  - 032
A1  - Arean, Daniel
AU  - Landsteiner, Karl
AU  - Salazar Landea, Ignacio
AB  - 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 at finite temperature real black holes 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.
ER  -

@Article{10.21468/SciPostPhys.9.3.032,
	title={{Non-hermitian holography}},
	author={Daniel Areán and Karl Landsteiner and Ignacio Salazar Landea},
	journal={SciPost Phys.},
	volume={9},
	pages={032},
	year={2020},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.9.3.032},
	url={https://scipost.org/10.21468/SciPostPhys.9.3.032},
}

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Funders for the research work leading to this publication

Comunidad de Madrid
Secretaría de Estado de Investigacion, Desarrollo e Innovacion (through Organization: Ministerio de Economía, Industria y Competitividad / Ministry of Economy, Industry and Competitiveness [MINECO])