出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：We present numerical results for U
1
gauge theory in 2d and 4d spaces involving a noncommutative
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 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.
