Influence of matter fields on the (de-)confining properties of the 3d Georgi-Glashow model

TL;DR

This paper investigates how matter fields affect the confining properties and phase transitions of the 3d Georgi-Glashow model, revealing quantitative changes in string tension and critical temperatures influenced by matter content.

Contribution

It provides a detailed analysis of the impact of matter fields on confinement and deconfinement, including corrections to the potential and critical flavor numbers for phase transitions.

Findings

Matter fields increase the 1/R-term coefficient in the potential.

String tension receives exponentially small positive correction.

Critical number of flavors for deconfinement depends on the BPS-limit, aligning with 4d instanton-liquid model results.

Abstract

The influence of various matter fields on the confining and finite-temperature properties of the (2+1)d Georgi-Glashow model is explored. At zero temperature, these fields are W-bosons, which play the role of heavy nodes, through which the quark-antiquark string passes. This fact is shown to increase by a factor $4\sqrt{2}$ the absolute value of the coefficient at the 1/R-term in the large-distance potential with respect to that of the Nambu-Goto string in 3d. The string tension also acquires a positive correction, which is, however, exponentially small. At finite temperature, the matter fields of interest are massless fundamental quarks, which diminish the deconfinement critical temperature by way of an additional attraction of a monopole and an antimonopole inside their molecules through the quark zero modes. It is demonstrated that, outside the BPS-limit, when the number of massless flavors is 4 or larger, the deconfinement phase transition occurs already at the temperatures of the order of the temperature of dimensional reduction. In the BPS limit, this critical number of flavors is 3. Since the temperature of dimensional reduction is exponenetially small and since monopoles are instantons in (2+1)d, these numbers can be compared with the one in the instanton-liquid model of 4d QCD, at which the chiral phase transition occurs at a vanishingly small temperature. The latter number is known to be of the order of 5, so that the results of the two models are quite close to each other.