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

Wolfgang Bietenholz, Antonio Bigarini, Jun Nishimura, Yoshiaki Susaki, Alessandro Torrielli, Jan Volkholz

Research output: Chapter in Book/Report/Conference proceedingChapter


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.
Original languageEnglish
Title of host publicationPoS LATTICE 2007
Publication statusPublished - 14 Aug 2007

Bibliographical note

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


  • hep-lat
  • astro-ph
  • hep-th

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