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Simulating U(1) gauge theory in a non-commutative space

Presenter: Wolfgang Bietenholz — DESY Zeuthen

W. Bietenholz, A. Bigarini, J. Nishimura, Y. Susaki, A. Torrielli, J. Volkholz

We present numerical studies of U(1) gauge theory in 2d and 4d spaces involving a non-commutative plane. Simulations are feasible thanks to the rigorous map of the non-commutative plane onto a twisted matrix model. In d=2 it was a long-standing issue if Wilson loops are invariant under area-preserving diffeomorphisms. We show that non-perturbatively this invariance breaks, in contrast to the commutative plane. In both cases, d=2 and d=4, we extrapolate of our results to the continuum and infinite volume by means of a double scaling limit. In d=4 this limit leads to a phase which is not affected by the perturbatively known IR instability. Therefore the photon may survive in a non-commutative world. Our results for its dispersion relation could be confronted with experimental data in the near future.