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

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

2007-08-14

arxiv.org/abs/0708.1857v2

PoSLAT2007:049,2007

Physics

High Energy Physics

High Energy Physics - Lattice

7 pages, 6 figures, talk presented by W.B. at LATTICE07

Scientific paper

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). In both cases, d=2 and d=4, we extrapolate our results to the continuum and infinite 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.

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