Non-Douglas-Kazakov phase transition of two-dimensional generalized Yang-Mills theories

TL;DR

This paper investigates a new type of phase transition in two-dimensional generalized Yang-Mills theories, occurring when the density becomes negative, which differs from the well-known Douglas-Kazakov transition, and analyzes their structure and order.

Contribution

It introduces and analyzes a novel phase transition in generalized Yang-Mills theories caused by negative density regions, expanding understanding beyond the traditional Douglas-Kazakov transition.

Findings

The new phase transition typically has order three.

It is caused by the density becoming negative in some regions.

Models with different transition orders can be constructed.

Abstract

In two-dimensional Yang-Mills and generalized Yang-Mills theories for large gauge groups, there is a dominant representation determining the thermodynamic limit of the system. This representation is characterized by a density the value of which should everywhere be between zero and one. This density itself is determined through a saddle-point analysis. For some values of the parameter space, this density exceeds one in some places. So one should modify it to obtain an acceptable density. This leads to the well-known Douglas-Kazakov phase transition. In generalized Yang-Mills theories, there are also regions in the parameter space where somewhere this density becomes negative. Here too, one should modify the density so that it remains nonnegative. This leads to another phase transition, different from the Douglas-Kazakov one. Here the general structure of this phase transition is studied, and it is shown that the order of this transition is typically three. Using carefully-chosen parameters, however, it is possible to construct models with phase-transition orders not equal to three. A class of these non-typical models are also studied.