The Master Field in Generalised $QC{D}_2$

Abstract

As an illustration of the formalism of the master field we consider generalised $QC{D}_2$. 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.

18 pages (big), 2 postscript figures, harvmac, epsf

References in corpus (7)

• Large $N$ Phase Transition in Continuum QCD${}_2$
• Mastering the Master Field
• Some Properties of Large $N$ Two Dimensional Yang--Mills Theory
• The String Theory Approach to Generalized 2D Yang-Mills Theory
• Stochastic Master Fields
• Generalized Two-Dimensional QCD
• Large N Phase Transitions and Multi-Critical Behaviour in Generalized 2D QCD

Cited by in corpus (5)

• Three proofs of the Makeenko-Migdal equation for Yang-Mills theory on the plane
• The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces
• The large-N limit for two-dimensional Yang-Mills theory
• Large N limit of Yang-Mills partition function and Wilson loops on compact surfaces
• Large-N limit of the generalized 2D Yang-Mills theory on cylinder