Large-N limit of the two-dimensoinal Yang-Mills theory on surfaces with boundaries

Details Large-N limit of the two-dimensoinal Yang-Mills theory on surfaces with boundaries Large-N limit of the two-dimensoinal Yang-Mills theory on surfaces with boundaries

2004-04-02

arxiv.org/abs/hep-th/0404009v2

Nucl.Phys. B696 (2004) 55-65

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX2e

Scientific paper

10.1016/j.nuclphysb.2004.07.006

The large-N limit of the two-dimensional U$(N)$ Yang-Mills theory on an arbitrary orientable compact surface with boundaries is studied. It is shown that if the holonomies of the gauge field on boundaries are near the identity, then the critical behavior of the system is the same as that of an orientable surface without boundaries with the same genus but with a modified area. The diffenece between this effective area and the real area of the surface is obtained and shown to be a function of the boundary conditions (holonomies) only. A similar result is shown to hold for the group SU$(N)$ and other simple groups.

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