Quantum effective action from the AdS/CFT correspondence

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dc.creatorSkenderis, Kostas
dc.creatorSolodukhin, Sergey N.
dc.date1999-10-04
dc.date1999-10-19
dc.date.accessioned2026-07-07T10:54:08Z
dc.date.available2026-07-07T10:54:08Z
dc.descriptionWe obtain an Einstein metric of constant negative curvature given an arbitrary boundary metric in three dimensions, and a conformally flat one given an arbitrary conformally flat boundary metric in other dimensions. In order to compute the on-shell value of the gravitational action for these solutions, we propose to integrate the radial coordinate from the boundary till a critical value where the bulk volume element vanishes. The result, which is a functional of the boundary metric, provides a sector of the quantum effective action common to all conformal field theories that have a gravitational description. We verify that the so-defined boundary effective action is conformally invariant in odd (boundary) dimensions and has the correct conformal anomaly in even (boundary) dimensions. In three dimensions and for arbitrary static boundary metric the bulk metric takes a rather simple form. We explicitly carry out the computation of the corresponding effective action and find that it equals the non-local Polyakov action.
dc.description12 pages, latex, no figures; v2: minor improvements and two references added
dc.identifierhttps://arxiv.org/abs/hep-th/9910023
dc.identifierhttp://arxiv.org/abs/hep-th/9910023
dc.identifierPhys.Lett.B472:316-322,2000
dc.identifierdoi:10.1016/S0370-2693(99)01467-7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185711
dc.subjectHigh Energy Physics - Theory
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectDifferential Geometry
dc.titleQuantum effective action from the AdS/CFT correspondence
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