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28 March 2024
 
  » arxiv » hep-th/9912009

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Extremal Curves in 2+1-Dimensional Yang-Mills Theory
Peter Orland ; Gordon W. Semenoff ;
Date 1 Dec 1999
Journal Nucl.Phys. B576 (2000) 627-654
Subject hep-th
AffiliationGraduate Center and Baruch College, CUNY) and Gordon W. Semenoff (University of British Columbia
AbstractWe examine the structure of the potential energy of 2+1-dimensional Yang-Mills theory on a torus with gauge group SU(2). We use a standard definition of distance on the space of gauge orbits. A curve of extremal potential energy in orbit space defines connections satisfying a certain partial differential equation. We argue that the energy spectrum is gapped because the extremal curves are of finite length. Though classical gluon waves satisfy our differential equation, they are not extremal curves. We construct examples of extremal curves and find how the length of these curves depends on the dimensions of the torus. The intersections with the Gribov horizon are determined explicitly. The results are discussed in the context of Feynman’s ideas about the origin of the mass gap.
Source arXiv, hep-th/9912009
Other source [GID 889806] hep-th/9912009
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