Maxwell-Chern-Simons Scalar Electrodynamics at Two Loop

TL;DR

This paper analyzes the two-loop effective potential of Maxwell-Chern-Simons scalar electrodynamics, revealing spontaneous symmetry breaking and dimensional transmutation, with detailed renormalization group analysis.

Contribution

It provides a closed-form two-loop effective potential and clarifies the subtlety in defining pure Chern-Simons scalar electrodynamics, including the Coleman-Weinberg limit.

Findings

U(1) symmetry is spontaneously broken in the massless scalar case

Dimensional transmutation occurs in the Coleman-Weinberg limit

Renormalization group analysis is performed at two loops

Abstract

The Maxwell-Chern-Simons gauge theory with charged scalar fields is analyzed at two loop level. The effective potential for the scalar fields is derived in the closed form, and studied both analytically and numerically. It is shown that the U(1) symmetry is spontaneously broken in the massless scalar theory. Dimensional transmutation takes place in the Coleman-Weinberg limit in which the Maxwell term vanishes. We point out the subtlety in defining the pure Chern-Simons scalar electrodynamics and show that the Coleman-Weinberg limit must be taken after renormalization. Renormalization group analysis of the effective potential is also given at two loop.