paper

Discrete Noncommutative Gauge Theory

arXiv:hep-th/0101216 · doi:10.1142/S0217732301003474

Abstract

A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang-Mills theory is constructed and used to examine some generic properties of noncommutative quantum field theory, such as UV/IR mixing and the appearence of gauge-invariant open Wilson line operators. Morita equivalence in this class of models is derived and used to establish the generic relation between noncommutative gauge theory and twisted reduced models. Finite dimensional representations of the quotient conditions for toroidal compactification of matrix models are thereby exhibited. The coupling of noncommutative gauge fields to fundamental matter fields is considered and a large mass expansion is used to study properties of gauge-invariant observables. Morita equivalence with fundamental matter is also presented and used to prove the equivalence between the planar loop renormalizations in commutative and noncommutative quantum chromodynamics.

19 pages LaTeX; Based on invited lecture given at the Euroconference "Brane New World and Noncommutative Geometry", Villa Gualino, Torino, Italy, October 2-7 2000. To be published in the proceedings by World Scientific; Typos corrected, reference added

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