Large-N limit of the two-dimensinal Non-Local Yang-Mills theory on arbitrary surfaces with boundary

TL;DR

This paper investigates the large-N limit of two-dimensional non-local U(N) Yang-Mills theories on surfaces with boundaries, revealing that their phase structure matches that of boundary-less surfaces with a modified area, under certain boundary conditions.

Contribution

It extends the understanding of large-N limits of non-local Yang-Mills theories to surfaces with boundaries, showing phase structure equivalence with boundary-less cases under specific conditions.

Findings

Phase structure is the same as boundary-less surfaces with a modified area.

Results hold for holonomies near the identity on boundaries.

Applicable to both orientable and non-orientable surfaces.

Abstract

The large-N limit of the two-dimensional non-local 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, $U\simeq I$, 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 $V+\hat{A}$.