Simulation Results for U(1) Gauge Theory on Non-Commutative Spaces

Understand

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 invariance breaks, including the subgroup SL(2,R).