Confining Properties of Abelian(-Projected) Theories

TL;DR

This paper derives effective actions for Abelian-projected SU(2) and SU(3) gluodynamics, revealing interactions with electric strings and vortex lines, and connects 3D compact QED to the Abelian Higgs model, providing insights into confinement mechanisms.

Contribution

It introduces effective actions including monopole interactions and links 3D compact QED to the Abelian Higgs model, offering a physical interpretation of confining strings.

Findings

Effective actions contain monopole-current interactions with electric strings and vortices.

3D compact QED is a limit of the Abelian Higgs model with monopoles.

Bilocal field strength correlator aligns with the Stochastic Vacuum Model.

Abstract

Representations of the Abelian-projected SU(2)- and SU(3)-gluodynamics in terms of the magnetic monopole currents are derived. Besides the quadratic part, the obtained effective actions contain interactions of these currents with the world-sheets of electric strings in 4D or electric vortex lines in 3D. Next, we illustrate that 3D compact QED is a small gauge boson mass limit of 3D Abelian Higgs model with external monopoles and give a physical interpretation to the confining string theory as the integral over the monopole densities. Finally, we derive the bilocal field strength correlator in the weak-field limit of 3D compact QED, which turns out to be in line with the one predicted by the Stochastic Vacuum Model.