Supersymmetric non-Abelian non-commutative Chern-Simons theory

  • Ferrari A
  • Gomes M
  • Petrov A
 et al. 
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Abstract

In this work, we study the three-dimensional non-Abelian non-commutative 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 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 term receives a quantum correction while, in the matter sector, the Chern-Simons term is generated, inducing a shift in the classical Chern-Simons coefficient. © 2006 Elsevier B.V. All rights reserved.

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Authors

  • A. F. Ferrari

  • M. Gomes

  • A. Yu Petrov

  • A. J. da Silva

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