Phase structure of the large-N reduced gauge theory and generalized Weingarten model

TL;DR

This paper investigates the phase transitions and symmetry breaking patterns in a generalized large-N reduced gauge theory, providing insights into its phase structure and developing an efficient algorithm for its analysis.

Contribution

It introduces a generalized Weingarten model that captures the phase structure of large-N reduced gauge theories and presents an efficient computational method for studying these phases.

Findings

Sequential symmetry breaking and restoration observed as coupling constants vary.

The model exhibits clear phase transitions in the large-N limit.

An efficient algorithm enables detailed analysis of the phase structure.

Abstract

We study a generalization of Weingarten model reduced to a point, which becomes the large-N reduced U(N) gauge theory in a special limit. We find that the U(1)^d symmetry is broken one by one, and restored simultaneously as U(1)^d -> U(1)^{d-1} -> ... -> U(1) -> 1 -> U(1)^d as we change the coupling constants. In this model we can develop an efficient algorithm and we can see the phase structure of large-N reduced model clearly, and therefore this model would be useful for the study of the unitary model.