Order Parameter for Confinement in Large N Gauge Theories with Fundamental Matter

TL;DR

This paper introduces a gauge-invariant order parameter for the confinement-deconfinement transition in large N gauge theories with fundamental matter, based on a solvable 2D SU(N) model, clarifying the phase structure and representation spectrum gap.

Contribution

It defines a new order parameter for confinement in large N gauge theories with fundamental matter, linking phase transitions to representation spectrum gaps.

Findings

Identifies a gap in the spectrum of irreducible representations in the strong coupling phase.

Provides a physical interpretation of phases via test charge interactions.

Proposes a gauge-invariant order parameter for the phase transition.

Abstract

In a solvable model of two dimensional SU(N) (N \to \infty) gauge fields interacting with matter in both adjoint and fundamental representations we investigate the nature of the phase transition separating the strong and weak coupling regions of the phase diagram. By interpreting the large N solution of the model in terms of SU(N) representations it is shown that the strong coupling phase corresponds to a region where a gap occurs in the spectrum of irreducible representations. We identify a gauge invariant order parameter for the generalized confinement-deconfinement transition and give a physical meaning to each phase in terms of the interaction of a pair of test charges.