Confining strings and RG flow in the (2+1)-dimensional Georgi-Glashow model and its SU(3)-generalization

TL;DR

This paper investigates confining strings and renormalization group flow in the (2+1)-dimensional Georgi-Glashow model at finite temperature, revealing modifications to the Debye mass, monopole potential, and Higgs mass scaling, with extensions to SU(3).

Contribution

It provides a detailed analysis of RG flow effects on confining strings and Higgs mass in the (2+1)D Georgi-Glashow model, including the SU(3) generalization, under specific coupling conditions.

Findings

Modified Debye mass of the dual photon at finite temperature.

Altered monopole density potential and string coupling constants.

Higgs mass scaling governed by a novel RG equation, remaining small compared to electric coupling.

Abstract

Confining strings and RG flow at finite temperature are investigated in the (2+1)-dimensional Georgi-Glashow model. This is done in the limit when the electric coupling constant is much larger than the square root of mass of the Higgs field, but much smaller than the vacuum expectation value of this field. The modification of the Debye mass of the dual photon with respect to the case when it is considered to be negligibly small compared to the Higgs mass, is found. Analogous modifications of the potential of monopole densities and string coupling constants are found. At finite temperature, the mass of the Higgs field scales according to a novel RG equation. It is checked that in the limit when the original theory is reduced by the RG flow to the 2D XY model, the so-evolved Higgs mass is still much smaller than the squared electric coupling constant. The SU(3)-theory of confining strings is also discussed within the same approximations.