Area-preserving diffeomorphisms in gauge theory on a non-commutative plane: a lattice study

We consider Yang-Mills theory with the U(1) gauge group on a noncommutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2, R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results are consistent with the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2, R) symmetry does not persist either.