Noncommutative Two-Dimensional Gauge Theories

Abstract

We elaborate on the dynamics of noncommutative two-dimensional gauge field theories. We consider U(N) gauge theories with fermions in either the fundamental or the adjoint representation. Noncommutativity leads to a rather non-trivial dependence on theta (the noncommutativity parameter) and to a rich dynamics. In particular the mass spectrum of the noncommutative U(1) theory with adjoint matter is similar to that of ordinary (commutative) two-dimensional large-N SU(N) gauge theory with adjoint matter. The noncommutative version of the 't Hooft model receives a non-trivial contribution to the vacuum polarization starting from three-loops order. As a result the mass spectrum of the noncommutative theory is expected to be different from that of the commutative theory.

11 pages, LaTex. 4 eps figures

References in corpus (1)

• On the mass spectrum of noncommutative Schwinger model in Euclidean ${\mathbb{R}}^2$ space

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• Study of the photon's pole structure in the noncommutative Schwinger model
• Dynamical generation of mass in the noncommutative supersymmetric Schwinger model
• The role of the Seiberg-Witten field redefinition in renormalization of noncommutative chiral electrodynamics