Phase transitions of Large-N two-dimensional Yang-Mills and generalized Yang-Mills theories in the double scaling limit

TL;DR

This paper investigates phase transitions in large-N two-dimensional Yang-Mills and generalized Yang-Mills theories under a double-scaling limit where the manifold's area depends on N, revealing different transition orders and finite-size effects.

Contribution

It introduces a detailed analysis of phase transitions and finite-size scalings in large-N Yang-Mills theories with a variable area in the double-scaling limit.

Findings

Different orders of phase transitions depending on area-N dependence

Finite-size scaling behaviors characterized for large but finite N

Explicit determination of dominant representations as a function of area

Abstract

The large-N behavior of Yang-Mills and generalized Yang-Mills theories in the double-scaling limit is investigated. By the double-scaling limit, it is meant that the area of the manifold on which the theory is defined, is itself a function of N. It is shown that phase transitions of different orders occur, depending on the functional dependence of the area on N. The finite-size scalings of the system are also investigated. Specifically, the dependence of the dominant representation on A, for large but finite N is determined.