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Modular discretization of the AdS2/CFT1 Holography

We propose a finite discretization for the black hole geometry and dynamics. We realize our proposal, in the case of extremal black holes, for which the radial and temporal near horizon geometry is known to be AdS$_2=SL(2,\mathbb{R})/SO(1,1,\mathbb{R})$. We implement its discretization by replacing...

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Detalles Bibliográficos
Autores principales: Axenides, Minos, Floratos, E.G., Nicolis, S.
Lenguaje:eng
Publicado: 2013
Materias:
Acceso en línea:https://dx.doi.org/10.1007/JHEP02(2014)109
http://cds.cern.ch/record/1557710
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author Axenides, Minos
Floratos, E.G.
Nicolis, S.
author_facet Axenides, Minos
Floratos, E.G.
Nicolis, S.
author_sort Axenides, Minos
collection CERN
description We propose a finite discretization for the black hole geometry and dynamics. We realize our proposal, in the case of extremal black holes, for which the radial and temporal near horizon geometry is known to be AdS$_2=SL(2,\mathbb{R})/SO(1,1,\mathbb{R})$. We implement its discretization by replacing the set of real numbers $\mathbb{R}$ with the set of integers modulo $N$, with AdS$_2$ going over to the finite geometry AdS$_2[N]=SL(2,\mathbb{Z}_N)/SO(1,1,\mathbb{Z}_N)$. We model the dynamics of the microscopic degrees of freedom by generalized Arnol'd cat maps, ${\sf A}\in SL(2,\mathbb{Z}_N)$, which are isometries of the geometry at both the classical and quantum levels. These exhibit well studied properties of strong arithmetic chaos, dynamical entropy, nonlocality and factorization in the cutoff discretization $N$, which are crucial for fast quantum information processing. We construct, finally, a new kind of unitary and holographic correspondence, for AdS$_2[N]$/CFT$_1[N]$, via coherent states of both the bulk and boundary geometries.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2013
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spelling cern-15577102022-08-10T20:39:55Zdoi:10.1007/JHEP02(2014)109http://cds.cern.ch/record/1557710engAxenides, MinosFloratos, E.G.Nicolis, S.Modular discretization of the AdS2/CFT1 HolographyParticle Physics - TheoryWe propose a finite discretization for the black hole geometry and dynamics. We realize our proposal, in the case of extremal black holes, for which the radial and temporal near horizon geometry is known to be AdS$_2=SL(2,\mathbb{R})/SO(1,1,\mathbb{R})$. We implement its discretization by replacing the set of real numbers $\mathbb{R}$ with the set of integers modulo $N$, with AdS$_2$ going over to the finite geometry AdS$_2[N]=SL(2,\mathbb{Z}_N)/SO(1,1,\mathbb{Z}_N)$. We model the dynamics of the microscopic degrees of freedom by generalized Arnol'd cat maps, ${\sf A}\in SL(2,\mathbb{Z}_N)$, which are isometries of the geometry at both the classical and quantum levels. These exhibit well studied properties of strong arithmetic chaos, dynamical entropy, nonlocality and factorization in the cutoff discretization $N$, which are crucial for fast quantum information processing. We construct, finally, a new kind of unitary and holographic correspondence, for AdS$_2[N]$/CFT$_1[N]$, via coherent states of both the bulk and boundary geometries.We propose a finite discretization for the black hole geometry and dynamics. We realize our proposal, in the case of extremal black holes, for which the radial and temporal near horizon geometry is known to be AdS$_2=SL(2,\mathbb{R})/SO(1,1,\mathbb{R})$. We implement its discretization by replacing the set of real numbers $\mathbb{R}$ with the set of integers modulo $N$, with AdS$_2$ going over to the finite geometry AdS$_2[N]=SL(2,\mathbb{Z}_N)/SO(1,1,\mathbb{Z}_N)$. We model the dynamics of the microscopic degrees of freedom by generalized Arnol'd cat maps, ${\sf A}\in SL(2,\mathbb{Z}_N)$, which are isometries of the geometry at both the classical and quantum levels. These exhibit well studied properties of strong arithmetic chaos, dynamical entropy, nonlocality and factorization in the cutoff discretization $N$, which are crucial for fast quantum information processing. We construct, finally, a new kind of unitary and holographic correspondence, for AdS$_2[N]$/CFT$_1[N]$, via coherent states of both the bulk and boundary geometries.arXiv:1306.5670CERN-PH-TH-2013-149CERN-PH-TH-2013-149oai:cds.cern.ch:15577102013-06-24
spellingShingle Particle Physics - Theory
Axenides, Minos
Floratos, E.G.
Nicolis, S.
Modular discretization of the AdS2/CFT1 Holography
title Modular discretization of the AdS2/CFT1 Holography
title_full Modular discretization of the AdS2/CFT1 Holography
title_fullStr Modular discretization of the AdS2/CFT1 Holography
title_full_unstemmed Modular discretization of the AdS2/CFT1 Holography
title_short Modular discretization of the AdS2/CFT1 Holography
title_sort modular discretization of the ads2/cft1 holography
topic Particle Physics - Theory
url https://dx.doi.org/10.1007/JHEP02(2014)109
http://cds.cern.ch/record/1557710
work_keys_str_mv AT axenidesminos modulardiscretizationoftheads2cft1holography
AT floratoseg modulardiscretizationoftheads2cft1holography
AT nicoliss modulardiscretizationoftheads2cft1holography