Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory

The classical analysis of Kazakov and Kostov of the Makeenko-Migdal loopequation in two-dimensional gauge theory leads to usual partial differentialequations with respect to the areas of windows formed by the loop. We extendthis treatment to the case of U(N) Yang-Mills defined on the noncommutativeplane. We deal with all the subtleties which arise in their two-dimensionalgeometric procedure, using where needed results from the perturbativecomputations of the noncommutative Wilson loop available in the literature. Theopen Wilson line contribution present in the non-commutative version of theloop equation drops out in the resulting usual differential equations. Theseequations for all N have the same form as in the commutative case for N toinfinity. However, the additional supplementary input from factorizationproperties allowing to solve the equations in the commutative case is no longervalid.Comment: 20 pages, 3 figures, references added, small clarifications adde