Anti-de Sitter Space, Thermal Phase Transition, and Confinement in Gauge Theories-英文文献.pdf

hep-th/9803131, IASSNS-HEP-98/21 Anti-de Sitter Space, Thermal Phase 8 Transition, And Confinement In Gauge Theories 9 9 1 r a M Edward Witten 6 1 School of Natural Sciences, Institute for Advanced Study 1 Olden Lane, Princeton, NJ 08540, USA v 1 3 1 The correspondence between supergravity (and string theory) on AdS space and 3 0 boundary conformal field theory relates the thermodynamics of N = 4 super Yang-Mills 8 9 theory in four dimensions to the thermodynamics of Schwarzschild black holes in Anti-de / h Sitter space. In this description, quantum phenomena such as the spontaneous breaking t - p of the center of the gauge group, magnetic confinement, and the mass gap are coded in e h classical geometry. The correspondence makes it manifest that the entropy of a very large : v AdS Schwarzschild black hole must scale “holographically” with the volume of its horizon. i X By similar methods, one can also make a speculative proposal for the description of large r a N gauge theories in four dimensions without supersymmetry. March, 1998 1. Introduction Understanding the large N behavior of gauge theories in four dimensions is a classic and important problem [1]. The structure of the “planar diagrams” that dominate the large N limit gave the first clue that this problem might be solved by interpreting four- dimensional large N gauge theory as a string theory. Attempts in this direction have led to many insights relevant to critical string theory; for an account of the status, see [2]. Recently, motivated by studies of interactions of branes with