On the invariance under area preserving diffeomorphisms of   noncommutative Yang-Mills theory in two dimensions
  We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations. 
A. Bassetto, G. De Pol, A. Torrielli, F. Vian