The paper discusses the correspondence between supergravity (and string theory) on Anti-de Sitter (AdS) space and boundary conformal field theory (CFT), focusing on the $\mathcal{N}=4$ super Yang-Mills theory in four dimensions. This correspondence relates the thermodynamics of the $\mathcal{N}=4$ theory to the thermodynamics of Schwarzschild black holes in AdS space. The paper explores several key phenomena, including the spontaneous breaking of the center of the gauge group, magnetic confinement, and the mass gap, which are coded in classical geometry. It demonstrates that the entropy of a large AdS Schwarzschild black hole scales holographically with the volume of its horizon, aligning with the Bekenstein-Hawking entropy formula.
The paper also applies similar methods to propose a framework for studying large $N$ gauge theories in four dimensions without supersymmetry. This proposal involves compactifying a six-dimensional $(0,2)$ theory with $(1,0)$ supersymmetry on two circles, resulting in a four-dimensional $SU(N)$ gauge theory. By breaking supersymmetry by taking fermions to be antiperiodic on one of the circles, the theory becomes a pure $SU(N)$ gauge theory, which can be used to study confinement and the mass gap. The paper concludes by discussing the high-temperature behavior of the $\mathcal{N}=4$ theory, including the behavior of temporal and spatial Wilson lines, and the existence of a mass gap.The paper discusses the correspondence between supergravity (and string theory) on Anti-de Sitter (AdS) space and boundary conformal field theory (CFT), focusing on the $\mathcal{N}=4$ super Yang-Mills theory in four dimensions. This correspondence relates the thermodynamics of the $\mathcal{N}=4$ theory to the thermodynamics of Schwarzschild black holes in AdS space. The paper explores several key phenomena, including the spontaneous breaking of the center of the gauge group, magnetic confinement, and the mass gap, which are coded in classical geometry. It demonstrates that the entropy of a large AdS Schwarzschild black hole scales holographically with the volume of its horizon, aligning with the Bekenstein-Hawking entropy formula.
The paper also applies similar methods to propose a framework for studying large $N$ gauge theories in four dimensions without supersymmetry. This proposal involves compactifying a six-dimensional $(0,2)$ theory with $(1,0)$ supersymmetry on two circles, resulting in a four-dimensional $SU(N)$ gauge theory. By breaking supersymmetry by taking fermions to be antiperiodic on one of the circles, the theory becomes a pure $SU(N)$ gauge theory, which can be used to study confinement and the mass gap. The paper concludes by discussing the high-temperature behavior of the $\mathcal{N}=4$ theory, including the behavior of temporal and spatial Wilson lines, and the existence of a mass gap.