Supersymmetric non-Abelian noncommutative Chern-Simons theory

TL;DR

This paper investigates the quantum properties of a three-dimensional non-Abelian supersymmetric noncommutative Chern-Simons model, demonstrating one-loop finiteness under certain conditions and analyzing quantum corrections to the effective action.

Contribution

It provides a superfield formulation proving one-loop finiteness for the pure gauge theory and explores quantum corrections in both gauge and matter sectors.

Findings

Green functions are one-loop finite in any gauge for fundamental representation.

Ultraviolet divergences cancel only in a special gauge with adjoint matter coupling.

Quantum corrections generate Maxwell and Chern-Simons terms, shifting the classical coefficient.

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.