Large-N limit of the two-dimensional Yang–Mills theory on surfaces with boundaries Original Research Article

The large-N limit of the two-dimensional image 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 difference 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 image and other simple groups.