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Perturbative Wilson loop in two-dimensional non-commutative Yang-Mills theory

Bassetto, A, Nardelli, G and Torrielli, A (2001) Perturbative Wilson loop in two-dimensional non-commutative Yang-Mills theory Nuclear Physics B, 617 (1-3). 308 - 320. ISSN 0550-3213


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We perform a perturbative ${\cal O}(g^4)$ Wilson loop calculation for the U(N) Yang-Mills theory defined on non-commutative one space - one time dimensions. We choose the light-cone gauge and compare the results obtained when using the Wu-Mandelstam-Leibbrandt ($WML$) and the Cauchy principal value ($PV$) prescription for the vector propagator. In the $WML$ case the $\theta$-dependent term is well-defined and regular in the limit $\theta \to 0$, where the commutative theory is recovered; it provides a non-trivial example of a consistent calculation when non-commutativity involves the time variable. In the $PV$ case, unexpectedly, the result differs from the $WML$ one only by the addition of two singular terms with a trivial $\theta$-dependence. We find this feature intriguing, when remembering that, in ordinary theories on compact manifolds, the difference between the two cases can be traced back to the contribution of topological excitations.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : 3 December 2001
Identification Number : 10.1016/S0550-3213(01)00477-1
Related URLs :
Additional Information : NOTICE: this is the author’s version of a work that was accepted for publication in Nuclear Physics B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nuclear Physics B, 617(1-3), 3 December 2001, DOI 10.1016/S0550-3213(01)00477-1.
Depositing User : Symplectic Elements
Date Deposited : 21 Feb 2012 15:50
Last Modified : 23 Sep 2013 18:57

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