Generating functional and large N limit on nonlocal 2D generalized Yang-Mills theories (nlgYM(2)'s)

Using the path integral method, we calculate the partition function and the generating functional (of the field strengths) on nonlocal generalized 2D Yang-Mills theories (nlgYM(2)'s), which are nonlocal in the auxiliary field . This has been considered before by Saaidi and Khorrami. Our calculations are done for general surfaces. We find a general expression for the free en ergy of W(phi) = phi (2k) in nlgYM(2) theories at the strong coupling phase (SCP) regime (A > A(c)) for large groups. In the specific phi (4) model, w e show that the theory has a third order phase transition.