Abstract

We review the basic properties of $$d$$ -dimensional conformal field theories (CFTs) and describe their relation to quantum gravitational theories on $$d+1$$ -dimensional anti-de Sitter ( $$\hbox{AdS}_{d+1}$$ ) space–times. We briefly review the ’t Hooft limit of $$U(N)$$ Yang–Mills theory, and then describe how an appropriate limit of type IIB superstring theory with D3-branes can be used to motivate a precise and computable correspondence between a four-dimensional conformal field theory and a quantum gravitational theory on $$\hbox{AdS}_5\times S^5$$ . We then discuss an extension of this construction in which probe branes on the AdS space–time are included.

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