Conformal Field Theory in More Than Two Dimensions
Higher-dimensional conformal field theories are prominent in the AdS/CFT correspondence, in which a gravitational theory in anti de Sitter space (AdS) is equivalent to a conformal field theory on the AdS boundary. Notable examples are d=4 N=4 super-Yang-Mills theory, which is dual to Type IIB string theory on AdS5 x S5, and d=3 N=6 super-Chern-Simons theory, which is dual to M-theory on AdS4 x S7. (The prefix "super" denotes supersymmetry, N denotes the degree of extended supersymmetry possessed by the theory, and d the number of space-time dimensions on the boundary.)
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