The abelian confinement mechanism revisited: New aspects of the Georgi–Glashow model

• We consider the problem of abelian confinement in the Georgi–Glashow model from a new perspective.
• We develop a many-body description of the degrees of freedom of this model in the background of monopole–instanton plasma.
• We use the many-body formalism to find an analytic expression of the potential between two probes at zero temperature.
• We also use a systematic approach to integrate out the W-bosons starting from the full relativistic partition function.
• This results in a three-dimensional two-component Coulomb gas with long range and Aharonov–Bohm phase interaction.

The confinement problem remains one of the most difficult problems in theoretical physics. An important step toward the solution of this problem is 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+12+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 along with a mean-field approximation, we calculate the 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