Spontaneous Symmetry Breaking at Two Loop in 3-d Massless Scalar Electrodynamics

TL;DR

This paper demonstrates that in 3D massless scalar electrodynamics with a $$6 coupling, spontaneous symmetry breaking occurs at two loops, with dimensional transmutation happening in pure Chern-Simons scalar electrodynamics, independent of gauge couplings.

Contribution

It shows spontaneous symmetry breaking at two loops in 3D scalar electrodynamics and reveals gauge-independent beta functions for the $$6 coupling.

Findings

Spontaneous symmetry breaking occurs at two loops.

Dimensional transmutation occurs in pure Chern-Simons scalar electrodynamics.

Beta function for $$6 coupling is gauge-independent.

Abstract

In three dimensional Maxwell-Chern-Simons massless scalar electrodynamics with $ \phi^6$ coupling, the $U(1)$ symmetry is spontaneously broken at two loop order regardless of the presence or absence of the Maxwell term. Dimensional transmutation takes place in pure Chern-Simons scalar electrodynamics. The beta function for the $\phi^6$ coupling is independent of gauge couplings.