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Nonperturbative Dynamics of Noncommutative Gauge Theory

J. Ambjorn·Y. M. Makeenko·J. Nishimura·R. J. Szabo
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Abstract

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*n_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 (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.

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J. Ambjorn, Y. M. Makeenko, J. Nishimura, R. J. Szabo. 2000-03-01. Nonperturbative Dynamics of Noncommutative Gauge Theory. https://doi.org/10.1016/s0370-2693(00)00391-9

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