The Master Field in Generalised $QCD_2$

TL;DR

This paper develops a formalism for the master field in generalized 2D QCD, enabling explicit computation of Wilson loop averages and deriving a governing Hopf equation for eigenvalue densities, thus providing new insights into the gauge field structure.

Contribution

It introduces a novel formalism for the master field in generalized QCD_2, allowing explicit calculations and deriving a governing Hopf equation for eigenvalue densities.

Findings

Explicit computation of Wilson loop averages for arbitrary contours.

Derivation of a Hopf equation governing eigenvalue density behavior.

Construction of the non-trivial master gauge field and field strengths.

Abstract

As an illustration of the formalism of the master field we consider generalised $QCD_2$. We show how Wilson Loop averages for an arbitrary contour can be computed explicitly and with some ease. A generalised Hopf equation is shown to govern the behaviour of the eigenvalue density of Wilson loops. The collective field description of the theory is therefore deduced. Finally, the non-trivial master gauge field and field strengths are obtained. These results do not seem easily accessible with conventional means.