Giovanni Landi, Fedele Lizzi, Richard J. Szabo
From Large N Matrices to the Noncommutative Torus
(71K, 23 pages. Latex )
ABSTRACT. We describe how and to what extent the noncommutative two-torus can be
approximated by a tower of finite-dimensional matrix geometries. The
approximation is carried out for both irrational and rational deformation
parameters by embedding the C^*-algebra of the noncommutative torus
into an approximately finite algebra. The construction is a rigorous
derivation of the recent discretizations of noncommutative gauge theories
using finite dimensional matrix models, and it shows precisely how the
continuum limits of these models must be taken. We clarify various
aspects of Morita equivalence using this formalism and describe some
applications to noncommutative Yang-Mills theory.