Generalizing the Coleman-Hill Theorem

TL;DR

This paper extends the Coleman-Hill theorem to systems with spontaneous symmetry breaking and fermions, showing that the correction to the Chern-Simons term remains unchanged across phases, with implications for nonabelian systems.

Contribution

It generalizes the Coleman-Hill theorem to include fermions and spontaneous symmetry breaking, demonstrating the invariance of the Chern-Simons correction across different phases.

Findings

The correction to the Chern-Simons term is identical in symmetric and Higgs phases.

The complicated correction in the Higgs phase simplifies to the same as in the symmetric phase.

Implications for nonabelian gauge systems are discussed.

Abstract

Following the work of Khare {\it et al}, we show that the generalization to systems with spontaneous symmetry breaking of the Coleman-Hill theorem to one-loop order, can be extended to the case including fermions with the most general interactions. Although the correction to the parity-odd part of the vacuum polarization looks complicated in the Higgs phase, it turns out that the correction to the Chern-Simons term is identical to that in the symmetric phase, with the difference coming only from the contribution of the would be Chern-Simons term. We also discuss the implication of our result to nonabelian systems.