3D Georgi-Glashow model and confining strings at zero and finite temperatures

TL;DR

This review explores the confining and finite-temperature behaviors of 3D SU(N) Georgi-Glashow and 4D compact QED models, deriving string representations and analyzing properties like string tensions, theta-terms, and effects of matter fields, with implications for QCD.

Contribution

It constructs the SU(N) confining string theory from the Georgi-Glashow model, including geometric properties and finite-temperature free energy, highlighting the role of negative stiffness and extensions with matter fields.

Findings

Derivation of string representations for confining theories.

Matching of finite-temperature string free energy with QCD at large N.

Identification of negative stiffness as stabilizing factor for confining strings.

Abstract

In this review, we discuss the confining and finite-temperature properties of the 3D SU(N) Georgi-Glashow model, and of 4D compact QED. At zero temperature, we derive string representations of both theories, thus constructing the SU(N)-version of Polyakov's theory of confining strings. We discuss the geometric properties of confining strings, as well as the appearance of the string theta-term from the field-theoretical one in 4D, and k-string tensions at N larger than 2. In particular, we point out the relevance of negative stiffness for stabilizing confining strings, an effect recently re-discovered in material science. At finite temperature, we present a derivation of the confining-string free energy and show that, at the one-loop level and for a certain class of string models in the large-D limit, it matches that of QCD at large N. This crucial matching is again a consequence of the negative stiffness. In the discussion of the finite-temperature properties of the 3D Georgi-Glashow model, in order to be closer to QCD, we mostly concentrate at the effects produced by some extensions of the model by external matter fields, such as dynamical fundamental quarks or photinos, in the supersymmetric generalization of the model.