Higgs-inspired corrections to the RG flow in the finite-temperature 3D Georgi-Glashow model and its SU(N)-generalization

TL;DR

This paper investigates how finite Higgs-boson mass affects the Berezinsky-Kosterlitz-Thouless RG flow in the finite-temperature 3D Georgi-Glashow model and its SU(N) generalization, finding minimal impact on critical properties.

Contribution

It derives leading-order corrections to the RG flow due to finite Higgs mass and analyzes the critical behavior in both SU(2) and SU(N) models, extending previous infinite-mass assumptions.

Findings

Critical temperature remains unaffected by Higgs mass finiteness.

RG invariance approximately holds in SU(N) models for N>2.

Higgs mass evolution is weak, allowing it to be treated as constant.

Abstract

The Berezinsky-Kosterlitz-Thouless (BKT) RG flow in the ensemble of monopoles existing in the finite-temperature (2+1)D Georgi-Glashow model is explored in the regime when the Higgs field is not infinitely heavy, but its mass is rather of the same order of magnitude as the mass of the W-boson. The corrections to the standard RG flow are derived to the leading order in the inverse mass of the Higgs boson. According to the obtained RG equations, the scaling of the free-energy density in the critical region and the value of the critical temperature of the phase transition are found to be unaffected by the finiteness of the Higgs-boson mass. The evolution of the Higgs mass itself is also investigated and shown to be rather weak, that enables one to treat this parameter as a constant. The same analysis is further performed in the SU(N)-case at N>2, where the RG invariance is demonstrated to hold only approximately, in a certain sense. Modulo this approximation, the critical behaviour of the SU(N)-model turns out to be identical to that of the SU(2)-one.