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

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 theelectric coupling constant is much larger than the square root of mass of theHiggs 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 casewhen it is considered to be negligibly small compared to the Higgs mass, isfound. Analogous modifications of the potential of monopole densities andstring coupling constants are found. At finite temperature, the mass of theHiggs field scales according to a novel RG equation. It is checked that in thelimit 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 electriccoupling constant. The SU(3)-theory of confining strings is also discussedwithin the same approximations.Comment: 14 pages, LaTeX2e, no figures, to appear in JHE