Wilson Loops in 2D Yang Mills: Euler characters and Loop equations

Abstract

We give a simple diagrammatic algorithm for writing the chiral large $N$ expansion of intersecting Wilson loops in $2D$ $SU(N)$ and $U(N)$Yang Mills theory in terms of symmetric groups, generalizing the result of Gross and Taylor for partition functions. We prove that these expansions compute Euler characters of a space of holomorphic maps from string worldsheets with boundaries. We prove that the Migdal-Makeenko equations hold for the chiral theory and show that they can be expressed as linear constraints on perturbations of the chiral $YM2$ partition functions. We briefly discuss finite $N$ , the non-chiral expansion, and higher dimensional lattice models.

55 pages, harvmac, 35 figures

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• Large N 2D Yang-Mills Theory and Topological String Theory
• Interacting Fermion Systems from Two Dimensional QCD
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• The String Partition Function for QCD on the Torus
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