Large-N limit of the two-dimensional non-local Yang–Mills theory on arbitrary surfaces with boundary

The large-N   limit of the two-dimensional non-local U(N)U(N) Yang–Mills theory on an orientable and non-orientable surface with boundaries is studied. For the case which the holonomies of the gauge group on the boundaries are near the identity, U≃IU≃I, it is shown that the phase structure of these theories is the same as that obtain for these theories on orientable and non-orientable surface without boundaries, with same genus but with a modified area V+Aˆ.