Nonperturbative dynamics of noncommutative gauge theory

We present a nonperturbative lattice formulation of noncommutative Yang–Mills theories in arbitrary even dimension. We show that lattice regularization of a noncommutative field theory requires finite lattice volume which automatically provides both an ultraviolet and an infrared cutoff. We demonstrate explicitly Morita equivalence of commutative U(p) gauge theory with p·nf flavours of fundamental matter fields on a lattice of size L with twisted boundary conditions and noncommutative U(1) gauge theory with nf species of matter on a lattice of size p·L with single-valued fields. We discuss the relation with twisted large N reduced models and construct observables in noncommutative gauge theory with matter.