Hidden relations of central charges and OPEs in holographic CFT

Abstract It is known that the (a, c) central charges in four-dimensional CFTs are linear combinations of the three independent OPE coefficients of the stress-tensor three-point function. In this paper, we adopt the holographic approach using AdS gravity as an effect field theory and consider higher-...

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Autores principales:	Yue-Zhou Li, H. Lü, Liang Ma
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	AdS-CFT Correspondence Gauge-gravity correspondence Classical Theories of Gravity Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/cc8d5c6a6e86455286dc7ee7c48b5e55
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spelling	oai:doaj.org-article:cc8d5c6a6e86455286dc7ee7c48b5e552021-11-21T12:40:57ZHidden relations of central charges and OPEs in holographic CFT10.1007/JHEP11(2021)1351029-8479https://doaj.org/article/cc8d5c6a6e86455286dc7ee7c48b5e552021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)135https://doaj.org/toc/1029-8479Abstract It is known that the (a, c) central charges in four-dimensional CFTs are linear combinations of the three independent OPE coefficients of the stress-tensor three-point function. In this paper, we adopt the holographic approach using AdS gravity as an effect field theory and consider higher-order corrections up to and including the cubic Riemann tensor invariants. We derive the holographic central charges and OPE coefficients and show that they are invariant under the metric field redefinition. We further discover a hidden relation among the OPE coefficients that two of them can be expressed in terms of the third using differential operators, which are the unit radial vector and the Laplacian of a four-dimensional hyperbolic space whose radial variable is an appropriate length parameter that is invariant under the field redefinition. Furthermore, we prove that the consequential relation c = 1/3ℓ eff ∂a/∂ℓ eff and its higher-dimensional generalization are valid for massless AdS gravity constructed from the most general Riemann tensor invariants.Yue-Zhou LiH. LüLiang MaSpringerOpenarticleAdS-CFT CorrespondenceGauge-gravity correspondenceClassical Theories of GravityConformal Field TheoryNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-28 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	AdS-CFT Correspondence Gauge-gravity correspondence Classical Theories of Gravity Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	AdS-CFT Correspondence Gauge-gravity correspondence Classical Theories of Gravity Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Yue-Zhou Li H. Lü Liang Ma Hidden relations of central charges and OPEs in holographic CFT
description	Abstract It is known that the (a, c) central charges in four-dimensional CFTs are linear combinations of the three independent OPE coefficients of the stress-tensor three-point function. In this paper, we adopt the holographic approach using AdS gravity as an effect field theory and consider higher-order corrections up to and including the cubic Riemann tensor invariants. We derive the holographic central charges and OPE coefficients and show that they are invariant under the metric field redefinition. We further discover a hidden relation among the OPE coefficients that two of them can be expressed in terms of the third using differential operators, which are the unit radial vector and the Laplacian of a four-dimensional hyperbolic space whose radial variable is an appropriate length parameter that is invariant under the field redefinition. Furthermore, we prove that the consequential relation c = 1/3ℓ eff ∂a/∂ℓ eff and its higher-dimensional generalization are valid for massless AdS gravity constructed from the most general Riemann tensor invariants.
format	article
author	Yue-Zhou Li H. Lü Liang Ma
author_facet	Yue-Zhou Li H. Lü Liang Ma
author_sort	Yue-Zhou Li
title	Hidden relations of central charges and OPEs in holographic CFT
title_short	Hidden relations of central charges and OPEs in holographic CFT
title_full	Hidden relations of central charges and OPEs in holographic CFT
title_fullStr	Hidden relations of central charges and OPEs in holographic CFT
title_full_unstemmed	Hidden relations of central charges and OPEs in holographic CFT
title_sort	hidden relations of central charges and opes in holographic cft
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/cc8d5c6a6e86455286dc7ee7c48b5e55
work_keys_str_mv	AT yuezhouli hiddenrelationsofcentralchargesandopesinholographiccft AT hlu hiddenrelationsofcentralchargesandopesinholographiccft AT liangma hiddenrelationsofcentralchargesandopesinholographiccft
_version_	1718418915390914560

Hidden relations of central charges and OPEs in holographic CFT

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