Anti-de Sitter space, thermal phase transition and confinement in gauge theories (Q2746864)

The problem which is discussed in this paper is to understand the high temperature behavior of \(N=4\) super-Yang-Mills theory. It is shown that the CFT/AdS correspondence implies, in the infinite volume limit, many expected but subtle quantum properties, including a nonzero expectation value for a temporal Wilson loop, an area law for spatial Wilson loop and a mass gap. The review of the relevant questions about gauge theories is given, and a few necessary properties of the Schwarzschild black holes on AdS space are developed. On the basis of the CFT/AdS correspondence it is demonstrated that the \(N=4\) theory at nonzero temperature has the claimed properties, especially the breaking of the center of the gauge group, magnetic confinement and the mass gap. The author presents a proposal for studying ordinary large \(N\) gauge theory in four dimensions (without supersymmetry or matter fields) via string theory.