Matrix Models, Large $N$ Limits and Noncommutative Solitons

Abstract

A survey of the interrelationships between matrix models and field theories on the noncommutative torus is presented. The discretization of noncommutative gauge theory by twisted reduced models is described along with a rigorous definition of the large $N$ continuum limit. The regularization of arbitrary noncommutative field theories by means of matrix quantum mechanics and its connection to noncommutative solitons is also discussed.