Dynamics of Wilson observables in non-commutative gauge theory

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 ʹt 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.