Effective abelian gauge theory for lattice gluodynamics and chromoelectric string

TL;DR

This paper develops an effective abelian gauge theory for lattice SU(2) gluodynamics, revealing a string representation of the chromoelectric flux tube and its relation to the underlying non-abelian gauge theory.

Contribution

It introduces a renormalizable, asymptotically free abelian gauge theory derived from lattice SU(2) gluodynamics, with a novel string representation involving ghosts on the string worldsheet.

Findings

The theory is equivalent to a compact abelian gauge theory with ghosts of charge 2.

The string representation provides a simple expression for the chromoelectric string action.

The theory is renormalizable and asymptotically free.

Abstract

The lattice SU(2) gluodynamics in the maximal abelian projection is reduced to the abelian theory, in which the natural small parameter exists. We show that in the zeroth order of the expansion in this parameter the theory is equivalent to the compact abelian gauge theory coupled to ghosts of charge 2. The theory is a renormalizable and asymptotically free. This theory is represented in the form of the theory of open string with the boundary consisting of the worldline of the quark. The ghosts live on the worldsheet of the string. The naive continuum limit of such string representation gives a simple expression for the chromoelectric string action.