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arXiv · hep-th/0312047

Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory

Harald Dorn·Alessandro Torrielli
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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additional supplementary input from factorization properties allowing to solve the equations in the commutative case is no longer valid.

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Harald Dorn, Alessandro Torrielli. 2003-12-11. Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory. https://doi.org/10.1088/1126-6708%2F2004%2F01%2F026

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