Structural and Dynamical Aspects of the AdS/CFT Correspondence: a Rigorous Approach

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dc.creatorRibeiro, Pedro Lauridsen
dc.date2007-12-03
dc.date2008-06-26
dc.date.accessioned2026-07-07T09:46:30Z
dc.date.available2026-07-07T09:46:30Z
dc.descriptionWe elaborate a detailed study of certain aspects of (a version of) the AdS/CFT correspondence, conjectured by Maldacena and Witten, between quantum field theories in a gravitational background given by an asymptotically anti-de Sitter (AAdS) spacetime, and conformally covariant quantum field theories in the latter's conformal infinity (in the sense of Penrose), aspects such that: (a) are independent from (the pair of) specific models in Quantum Field Theory, and (b) susceptible to a recast in a mathematically rigorous mould. We adopt as a starting point the theorem demonstrated by Rehren in the context of Local Quantum Physics (also known as Algebraic Quantum Field Theory) in anti-de Sitter (AdS) spacetimes, called algebraic holography or Rehren duality. The main body of the present work consists in extending Rehren's result to a reasonably general class of d-dimensional AAdS spacetimes (d>3), scrutinizing how the properties of such an extension are weakened and/or modified as compared to AdS spacetime, and probing how non-trivial gravitational effects manifest themselves in the conformal infinity's quantum theory. The language employed for the quantum theories relevant for our generalization of Rehren duality follows the functorial formulation of Local Quantum Physics due to Brunetti, Fredenhagen and Verch, extended afterwards by Sommer in order to incorporate boundary conditions.
dc.descriptionEnglish translation (with corrections) of the author's Ph.D. thesis (University of S. Paulo, Brazil, September 2007), originally written in Portuguese - see comments in page ii for more details. 201 pages, 7 figures. V3: an incorrect and ultimately irrelevant construction in Subsection 2.3.1 replaced by appropriate amendments, 1 extra reference and erratum
dc.identifierhttps://arxiv.org/abs/0712.0401
dc.identifierhttp://arxiv.org/abs/0712.0401
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163551
dc.subjectMathematical Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectDifferential Geometry
dc.subjectOperator Algebras
dc.subject81T05, 81T20, 53C50
dc.titleStructural and Dynamical Aspects of the AdS/CFT Correspondence: a Rigorous Approach
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