From Large N Matrices to the Noncommutative Torus

Details From Large N Matrices to the Noncommutative Torus From Large N Matrices to the Noncommutative Torus

1999-12-15

arxiv.org/abs/hep-th/9912130v1

Commun.Math.Phys. 217 (2001) 181-201

Physics

High Energy Physics

High Energy Physics - Theory

23 pages LaTeX2e

Scientific paper

10.1007/s002200000356

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 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.

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