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Large \(N\) field theories, string theory and gravity. (English) Zbl 1368.81009
Summary: We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the \(N=4\) supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and non-conformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.

MSC:
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T13 Yang-Mills and other gauge theories in quantum field theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83C57 Black holes
83E15 Kaluza-Klein and other higher-dimensional theories
83E30 String and superstring theories in gravitational theory
83E50 Supergravity
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