Generating Functional and Large N-Limit of Nonlocal 2D Generalized Yang-Mills Theories ($nlgYM_2$'s)

TL;DR

This paper calculates the partition function and free energy of nonlocal 2D generalized Yang-Mills theories using path integrals, revealing a third order phase transition in a specific model at large group limits.

Contribution

It provides a general expression for the free energy of $W()=^{2k}$ in nonlocal 2D Yang-Mills theories at strong coupling for large groups.

Findings

Derived a general formula for free energy in $nlgYM_2$ theories.

Identified a third order phase transition in the $^4$ model.

Analyzed the strong coupling phase for large gauge groups.

Abstract

Using the path integral method, we calculate the partition function and generating functional (of the field strengths) on the nonlocal generalized 2D Yang - Mills theories ($nlgYM_2$'s), which is nonlocal in auxiliary field [14]. Our calculations is done for general surfaces. We find a general expression for free energy 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, we show that the theory has a third order phase transition.