Nonperturbative dynamics of noncommutative gauge theory

We present a nonperturbative lattice formulation of noncommutative Yang-Mil ls theories in arbitrary even dimension. We show that lattice regularizatio n of a noncommutative field theory requires finite lattice volume which aut omatically provides both an ultraviolet and an infrared cutoff. We demonstr ate explicitly Morita equivalence of commutative U(p) gauge theory with p . n(f) flavours of fundamental matter fields on a lattice of size L with twi sted boundary conditions and noncommutative U(1) gauge theory with n(f) spe cies of matter on a lattice of size p L with single-valued fields. We discu ss the relation with twisted large N reduced models and construct observabl es in noncommutative gauge theory with matter. (C) 2000 Elsevier Science B. V. All rights reserved.