1999/11/16 by J. Ambjorn, Y. M. Makeenko, J. Nishimura +1 · 1 citation
Physics and Astronomy · #hep-th #hep-lat
paper · pdf · doi:10.1088/1126-6708/1999/11/029
published as JHEP 9911 (1999) 029 · 17 pp, Latex2e; Typos corrected, references added
arxiv created 1999/11/16 · arxiv updated 2009/11/30
We describe a unitary matrix model which is constructed from discrete analogs of the usual projective modules over the noncommutative torus and use it to construct a lattice version of noncommutative gauge theory. The model is a discretization of the noncommutative gauge theories that arise from toroidal compactification of Matrix theory and it includes a recent proposal for a non-perturbative definition of noncommutative Yang-Mills theory in terms of twisted reduced models. The model is interpreted as a manifestly star-gauge invariant lattice formulation of noncommutative gauge theory, which reduces to ordinary Wilson lattice gauge theory for particular choices of parameters. It possesses a continuum limit which maintains both finite spacetime volume and finite noncommutativity scale. We show how the matrix model may be used for studying the properties of noncommutative gauge theory.