Non-local 2D Generalized Yang-Mills theories on arbitrary surfaces with boundary

TL;DR

This paper analyzes non-local generalized 2D Yang-Mills theories on arbitrary surfaces with boundaries, revealing their phase structure and phase transitions, especially in the large-N limit, with specific results for the $ ext{phi}^2$ model.

Contribution

It derives the effective action for these theories near the identity gauge group and explores their phase structure on surfaces with boundaries, extending previous results to more general surfaces.

Findings

The phase structure is the same as on surfaces without boundaries in the large-N limit.

The $ ext{phi}^2$ model exhibits third order phase transitions only on specific surfaces.

Modified area parameters determine the phase transition points.

Abstract

The non-local generalized two dimensional Yang Mills theories on an arbitrary orientable and non-orientable surfaces with boundaries is studied. We obtain the effective action of these theories for the case which the gauge group is near the identity, $U\simeq I$. 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 obtain for these theories on orientable and non-orientable surface without boundaries. It is seen that the $\phi^2$ model of these theories on an arbitrary orientable and non-orientable surfaces with boundaries have third order phase transition only on $g=0$ and $r=1$ surfaces, with modified area $\tilde{A}+{\cal A}/2$ for orientable and $\bar{A}+\mathcal{A}$ for non-orientable surfaces respectivly.