The abelian confinement mechanism revisited: new aspects of the Georgi-Glashow model

TL;DR

This paper revisits the abelian confinement mechanism in the Georgi-Glashow model, providing new insights through many-body analysis and finite-temperature effects, revealing a complex potential and phase behavior relevant to confinement.

Contribution

It introduces a many-body description of effective degrees of freedom and a systematic finite-temperature analysis, connecting the model to a Coulomb gas and sine-Gordon model.

Findings

Exact potential between electric probes expressed via Meijer-G function.

Partition function describes a three-dimensional two-component Coulomb gas.

Near deconfinement, the system reduces to a two-dimensional sine-Gordon model.

Abstract

The confinement problem remains one of the most difficult problems in theoretical physics. An important step toward the solution of this problem is the Polyakov's work on abelian confinement. The Georgi-Glashow model is a natural testing ground for this mechanism which has been surprising us by its richness and wide applicability. In this work, we shed light on two new aspects of this model in 2+1 D. First, we develop a many-body description of the effective degrees of freedom. Namely, we consider a non-relativistic gas of W-bosons in the background of monopole-instanton plasma. Many-body treatment is a standard toolkit in condensed matter physics. However, we add a new twist by supplying the monopole-instantons as external background field. Using this construction, we calculate the exact form of the potential between two electric probes as a function of their separation. This potential is expressed in terms of the Meijer-G function which interpolates between logarithmic and linear behavior at small and large distances, respectively. Second, we develop a systematic approach to integrate out the effect of the W-bosons at finite temperature in the range 0<T<M_W, where M_W is the W-boson mass, starting from the full relativistic partition function of the Georgi-Glashow model. Using a heat kernel expansion that takes into account the non-trivial thermal holonomy, we show that the partition function describes a three-dimensional two-component Coulomb gas. We repeat our analysis using the many-body description which yields the same result and provides a check on our formalism. At temperatures close to the deconfinement temperature, the gas becomes essentially two-dimensional recovering the partition function of the dual sine-Gordon model that was considered in a previous work.