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

A. Bassetto·G. Nardelli·A. Torrielli
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Abstract

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 $θ$-dependent term is well-defined and regular in the limit $θ\to 0$, 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 $θ$-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.

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A. Bassetto, G. Nardelli, A. Torrielli. 2001-07-18. Perturbative Wilson loop in two-dimensional non-commutative Yang-Mills theory. https://doi.org/10.1016/s0550-3213(01)00477-1

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