Renormalization-group flow in the 3D Georgi-Glashow model

TL;DR

This paper investigates the renormalization-group flow in the finite-temperature 3D Georgi-Glashow model, deriving a new equation for Higgs mass evolution and analyzing its behavior near the phase transition.

Contribution

It introduces a novel RG flow equation for the Higgs mass and explores its implications in the 2D XY model limit of the theory.

Findings

Higgs mass remains small along certain RG flow separatrices near the phase transition.

Derived a new equation describing Higgs mass evolution in the RG flow.

Identified parameter ranges where Higgs mass stays much smaller than the squared electric coupling.

Abstract

The renormalization-group (RG) flow in the finite-temperature (2+1)-dimensional Georgi-Glashow model is explored. This is done in the limit when the squared electric coupling constant is much larger than the mass of the Higgs field. The novel equation describing the evolution of the Higgs mass is derived and integrated along the separatrices of the RG flow in the limit when the original theory reduces to the 2D XY model. In particular, it is checked that in the vicinity of the phase-transition point, there exists a range of parameters allowing to the Higgs mass evolved along some of the separatrices to remain much smaller than the squared electric coupling constant.