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

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.

Deconfining phase transition in the 3D Georgi–Glashow model with finite Higgs-boson mass

“…[6], the influence of the Higgs field to the dynamics of the Georgi-Glashow model has been studied both at zero and nonzero temperature. In particular, it has been found that the finiteness of the Higgs-boson mass does not change the value of the critical temperature of the monopole BKT phase transition.…”

“…However, in ref. [6] the effects of W-bosons have been disregarded, that makes the performed analysis incomplete. The aim of the present letter is to explore the influence of the Higgs-mediated interaction of monopoles to the deconfining phase transition with the account for W-bosons.…”

HIGGS-INSPIRED CORRECTIONS TO THE RG FLOW IN THE FINITE-TEMPERATURE 3D GEORGI–GLASHOW MODEL AND ITS SU(N)-GENERALIZATION

“…Besides the investigations performed in the compact-QED limit of this model (where the Higgs boson is infinitely heavy), there have recently also been done several investigations of the Georgi-Glashow model beyond that limit [2,3]. The analysis of ref.…”

“…The analysis of ref. [2] has been carried out in the Bogomolny-Prasad-Sommerfield (BPS) limit [4], that is the limit where the Higgs field is much lighter than the W-boson. In that paper, the theory has been investigated both at zero and nonzero temperatures.…”

“…As well as in ref. [2], there will be derived the RG equation describing the evolution of m H . However, due to the largeness of m H with respect to the characteristic momentum scale we are working at (since m H is of the order of the UV cutoff m W ), this evolution will be shown to be rather weak.…”