Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory

Abstract

The classical analysis of Kazakov and Kostov of the Makeenko-Migdal loop equation in two-dimensional gauge theory leads to usual partial differential equations with respect to the areas of windows formed by the loop. We extend this treatment to the case of U(N) Yang-Mills defined on the noncommutative plane. We deal with all the subtleties which arise in their two-dimensional geometric procedure, using where needed results from the perturbative computations of the noncommutative Wilson loop available in the literature. The open Wilson line contribution present in the non-commutative version of the loop equation drops out in the resulting usual differential equations. These equations for all N have the same form as in the commutative case for N to infinity. However, the additional supplementary input from factorization properties allowing to solve the equations in the commutative case is no longer valid.

20 pages, 3 figures, references added, small clarifications added

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Cited by in corpus (8)

• Numerical Results for U(1) Gauge Theory on 2d and 4d Non-Commutative Spaces
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Morita Duality and Noncommutative Wilson Loops in Two Dimensions
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 1. Perturbative Expansion
• On the invariance under area preserving diffeomorphisms of noncommutative Yang-Mills theory in two dimensions
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/θExpansion
• Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory