The non-local 2D generalized Yang–Mills theories on arbitrary surfaces with boundaries

Abstract

The non-local generalized two-dimensional Yang–Mills theories on arbitrary orientable and non-orientable surfaces with boundaries is studied. We obtain the effective action of these theories for the case when the holonomy of the gauge field around the boundary components is near the identity, U≃I. Furthermore, by obtaining the effective action at the large-N limit, it is shown that the phase structure of these theories is the same as that obtained for these theories on orientable and non-orientable surfaces without boundaries. It is seen that the ϕ2 model of these theories on arbitrary orientable and non-orientable surfaces with boundaries have third-order phase transition only on g=0 and r=1 surfaces, with modified area for orientable and for non-orientable surfaces, respectively.