The Chern-Simons Coefficient in Supersymmetric Non-abelian Chern-Simons Higgs Theories

TL;DR

This paper calculates quantum corrections to the Chern-Simons coefficient in supersymmetric non-abelian Chern-Simons Higgs theories, revealing that corrections vanish in N=3 supersymmetry and are identical across phases due to supersymmetry.

Contribution

It provides the first detailed calculation of quantum corrections to the Chern-Simons coefficient in supersymmetric non-abelian Higgs theories with matter in the fundamental representation.

Findings

Quantum corrections vanish for N=3 supersymmetry.

Corrections are identical in symmetric and Higgs phases.

Results are expected to extend to adjoint Higgs representations.

Abstract

By taking into account the effect of the would be Chern-Simons term, we calculate the quantum correction to the Chern-Simons coefficient in supersymmetric Chern-Simons Higgs theories with matter fields in the fundamental representation of SU(n). Because of supersymmetry, the corrections in the symmetric and Higgs phases are identical. In particular, the correction is vanishing for N=3 supersymmetric Chern-Simons Higgs theories. The result should be quite general, and have important implication for the more interesting case when the Higgs is in the adjoint representation.