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Finite N Matrix Models of Noncommutative Gauge Theory
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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.
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Quantization of Algebraic Varieties Defined by Casimir Polynomials via Matrix Regularization: Fuzzy $S^7$ and Beyond
A weak matrix regularization of any single-Casimir level set of a compact semisimple Lie algebra is built from reducible representations whose coadjoint orbits densely fill the variety, with fuzzy S^7 worked out explicitly.
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