Comments on the Morita Equivalence

Abstract

It is known that noncommutative Yang-Mills theory with periodical boundary conditions on torus at the rational value of the noncommutativity parameter is Morita equivalent to the ordinary Yang-Mills theory with twisted boundary conditions on dual torus. We present simple derivation of this fact. We describe one-to-one correspondence between and gauge invariant observables in these two theories. In particular, we show that under Morita map Polyakov loops in the ordinary YM theory go to the open noncommutative Wilson loops discovered by Ishibashi, Iso, Kawai and Kutazawa.