Large-N transitions for generalized Yang-Mills theories in 1+1 dimensions

TL;DR

This paper maps the phase structure of large-N generalized Yang-Mills theories in 1+1 dimensions, revealing multiple phase transitions and sub-phases, including the Douglas-Kazakov and cut-off transitions, with detailed analysis for a specific quartic-plus-quadratic model.

Contribution

It provides a comprehensive analysis of the phase diagram for generalized Yang-Mills theories in 1+1 dimensions, including explicit computations and identification of various phase transitions.

Findings

Identification of three main phases: dilute, strongly interacting, and degenerate.

Presence of Douglas-Kazakov and cut-off transitions separating these phases.

Second-order phase transitions within the degenerate phase.

Abstract

We describe the entire phase structure of a large number of colour generalized Yang-Mills theories in 1+1 dimensions. This is illustrated by the explicit computation for a quartic plus quadratic model. We show that the Douglas-Kazakov and cut-off transitions are naturally present for generalized Yang-Mills theories separating the phase space into three regions: a dilute one a strongly interacting one and a degenerate one. Each region is separated into sub-phases. For the first two regions the transitions between sub-phases are described by the Jurekiewicz-Zalewski analysis. The cut-off transition and degenerated phase arise only for a finite number of colours. We present second-order phase transitions between sub-phases of the degenerate phase.