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Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory

Dorn, H and Torrielli, A (2004) Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory Journal of High Energy Physics, 01.


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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additional supplementary input from factorization properties allowing to solve the equations in the commutative case is no longer valid.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Dorn, H
Torrielli, A
Date : 1 January 2004
DOI : 10.1088/1126-6708/2004/01/026
Related URLs :
Additional Information : Copyright 2004 Institute of Physics. This is the author's accepted manuscript.
Depositing User : Symplectic Elements
Date Deposited : 08 Feb 2012 16:04
Last Modified : 31 Oct 2017 14:17

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