Large-N limit of the non-local 2D Yang-Mills and generalized Yang-Mills theories on a cylinder

TL;DR

This paper investigates the large-N behavior of non-local 2D Yang-Mills and generalized Yang-Mills theories on a cylinder, revealing similarities to local theories with an effective area, and identifies critical areas for certain boundary conditions.

Contribution

It introduces the large-N analysis of nonlocal YM$_2$ and gYM$_2$ on a cylinder, showing their behavior parallels local theories with an effective area, and determines critical areas for specific boundary conditions.

Findings

Behavior similar to local theories with an effective area

Critical areas for nonlocal YM$_2$ with boundary conditions

Large-N limit analysis of nonlocal gauge theories

Abstract

The large-group behavior of the nonlocal YM$_2$'s and gYM$_2$'s on a cylinder or a disk is investigated. It is shown that this behavior is similar to that of the corresponding local theory, but with the area of the cylinder replaced by an effective area depending on the dominant representation. The critical areas for nonlocal YM$_2$'s on a cylinder with some special bounary conditions are also obtained.