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 non-commutative 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.Comment: 28 pages, 15 figures, published versio

P oS(LATTICE 2007)049 Simulation Results for U 1 Gauge Theory on Non-Commutative Spaces

We present numerical results for U 1 gauge theory in 2d and 4d spaces involving a non-commutative plane. Simulations are feasible thanks to a mapping of the non-commutative plane onto a twisted matrix model. In d 2 it was a long-standing issue if Wilson loops are (partially) invariant under area-preserving diffeomorphisms. We show that non-perturbatively this invari-ance breaks, including the subgroup SL 2 R . In both cases, d 2 and d 4, we extrapolate our results to the continuum and innite volume by means of a Double Scaling Limit. In d 4 this limit leads to a phase with broken translation symmetry, which is not affected by the perturbatively known IR instability. Therefore the photon may survive in a non-commutative world. The XXV International Symposium on Lattice Field Theor