Dynamics of Wilson Observables in Non-Commutative Gauge Theory

Abstract

An equation for the quantum average of the gauge invariant Wilson loop in non-commutative Yang-Mills theory with gauge group U(N) is obtained. In the 't Hooft limit, the equation reduces to the loop equation of ordinary Yang-Mills theory. At finite $N$, the equation involves the quantum averages of the additional gauge invariant observables of the non-commutative theory associated with open contours in space-time. We also derive equations for correlators of several gauge invariant (open or closed) Wilson lines. Finally, we discuss a perturbative check of our results.

12 pages, typo in formula (32) corrected

References in corpus (4)

• Wilson Loops in Noncommutative Yang Mills
• Lattice Gauge Fields and Discrete Noncommutative Yang-Mills Theory
• Finite N Matrix Models of Noncommutative Gauge Theory
• Gauge fields - strings duality and the loop equation

Cited by in corpus (9)

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• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 1. Perturbative Expansion
• Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory
• 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
• Solving loop equations by Hitchin systems via holography in large-N QCD_4
• Area preserving diffeomorphisms and Yang-Mills theory in two noncommutative dimensions