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Supersymmetric non-Abelian noncommutative Chern-Simons theory

A. F. Ferrari·M. Gomes·A. Yu. Petrov·A. J. da Silva
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Abstract

In this work, we study the three-dimensional non-Abelian noncommutative supersymmetric Chern-Simons model with the U(N) gauge group. Using a superfield formulation, we prove that, for the pure gauge theory, the Green functions are one-loop finite in any gauge, if the gauge superpotential belongs to the fundamental representation of $u(N)$; this result also holds when matter in the fundamental representation is included. However, the cancellation of both ultraviolet and ultraviolet/infrared infrared divergences only happens in a special gauge if the coupling of the matter is in the adjoint representation. We also look into the finite one-loop quantum corrections to the effective action: in the pure gauge sector the Maxwell together with its corresponding gauge fixing action are generated; in the matter sector, the Chern-Simons term is generated, inducing a shift in the classical Chern-Simons coefficient.

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A. F. Ferrari, M. Gomes, A. Yu. Petrov, A. J. da Silva. 2006-02-03. Supersymmetric non-Abelian noncommutative Chern-Simons theory. https://doi.org/10.1016/j.physletb.2006.05.031

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