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 (pn_f) flavours of fundamental matter fields on a lattice of size L with twisted boundary conditions and noncommutative U(1) gauge theory with n_f species of matter on a lattice of size (pL) with single-valued fields. We discuss the relation with twisted large N reduced models and construct observables in noncommutative gauge theory with matter.