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

Abstract

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.

27 pages, 2 figures

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• Numerical Results for U(1) Gauge Theory on 2d and 4d Non-Commutative Spaces
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Morita Duality and Noncommutative Wilson Loops in Two Dimensions
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• On the invariance under area preserving diffeomorphisms of noncommutative Yang-Mills theory in two dimensions
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/θExpansion
• Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
• Area-preserving diffeomorphisms in gauge theory on a non-commutative plane: a lattice study
• Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
• Area preserving diffeomorphisms and Yang-Mills theory in two noncommutative dimensions