Confinement in Gauge Theories from the Condensation of World-Sheet Defects in Liouville String

Details Confinement in Gauge Theories from the Condensation of World-Sheet Defects in Liouville String Confinement in Gauge Theories from the Condensation of World-Sheet Defects in Liouville String

1998-08-28

arxiv.org/abs/hep-th/9808172v1

Int.J.Mod.Phys.A14:3761-3788,1999

Physics

High Energy Physics

High Energy Physics - Theory

29 pages LATEX, three eps figures incorporated

Scientific paper

10.1142/S0217751X99001743

We present a Liouville-string approach to confinement in four-dimensional gauge theories, which extends previous approaches to include non-conformal theories. We consider Liouville field theory on world sheets whose boundaries are the Wilson loops of gauge theory, which exhibit vortex and spike defects. We show that world-sheet vortex condensation occurs when the Wilson loop is embedded in four target space-time dimensions, and show that this corresponds to the condensation of gauge magnetic monopoles in target space. We also show that vortex condensation generates a effective string tension corresponding to the confinement of electric degrees of freedom. The tension is independent of the string length in a gauge theory whose electric coupling varies logarithmically with the length scale. The Liouville field is naturally interpreted as an extra target dimension, with an anti-de-Sitter (AdS) structure induced by recoil effects on the gauge monopoles, interpreted as D branes of the effective string theory. Black holes in the bulk AdS space correspond to world-sheet defects, so that phases of the bulk gravitational system correspond to the different world-sheet phases, and hence to different phases of the four-dimensional gauge theory. Deconfinement is associated with a Berezinskii-Kosterlitz-Thouless transition of vortices on the Wilson-loop world sheet, corresponding in turn to a phase transition of the black holes in the bulk AdS space.

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