Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 1. Perturbative Expansion

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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27 pages, 2 figures

Scientific paper

10.1088/1126-6708/2004/07/044

We calculate quantum averages of Wilson loops (holonomies) in gauge theories on the Euclidean noncommutative plane, using a path-integral representation of the star-product. We show how the perturbative expansion emerges from a concise general formula and demonstrate its anomalous behavior at large parameter of noncommutativity for the simplest nonplanar diagram of genus 1. We discuss various UV/IR regularizations of the two-dimensional noncommutative gauge theory in the axial gauge and, using the noncommutative loop equation, construct a consistent regularization.

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