Simulation Results for U(1) Gauge Theory on Non-Commutative Spaces
Abstract
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.
Cite
@article{arxiv.0708.1857,
title = {Simulation Results for U(1) Gauge Theory on Non-Commutative Spaces},
author = {Wolfgang Bietenholz and Antonio Bigarini and Jun Nishimura and Yoshiaki Susaki and Alessandro Torrielli and Jan Volkholz},
journal= {arXiv preprint arXiv:0708.1857},
year = {2008}
}
Comments
7 pages, 6 figures, talk presented by W.B. at LATTICE07