Wilson loops in non-commutative Yang-Mills

Wc study the correlation functions of the Wilson loops in non-commutative Yang-Mills theory based upon its equivalence to twisted reduced models. We point out that there is a crossover at the non-commutativity scale. At large momentum scale, the Wilson loops in non-commmutative Yang-Mills represent extended objects. They coincide with those in ordinary Yang-Mills theory in a low energy limit. The correlation functions on D-branes in a IIB matrix model exhibit the identical crossover behavior. It is observed to be consistent with the supergravity description with running string coupling. We also explain that the results of Seiberg and Witten can be simply understood in our formalism. (C) 2000 Elsevier Science B.V. All rights reserved.