The gluon condensate in an effective SU(2) Yang-Mills theory

TL;DR

This paper derives a low energy effective SU(2) Yang-Mills theory using 1-loop renormalization group methods, incorporating Spin-Charge decomposition, and links solitonic configurations to glueball states.

Contribution

It presents a novel derivation of a low energy effective theory for SU(2) Yang-Mills, including the Spin-Charge decomposition and analysis of solitonic glueball configurations.

Findings

Effective low energy action computed at 1-loop.

Scalar potential has a Mexican hat shape.

Solitonic configurations correspond to glueball states.

Abstract

We make progress towards a derivation of a low energy effective theory for SU(2) Yang-Mills theory. This low energy action is computed to 1-loop using the renormalization group technique, taking proper care of the Slavnov-Taylor identities in the Maximal Abelian Gauge. After that, we perform the Spin-Charge decomposition in a way proposed by L.D. Faddeev and A.J. Niemi. The resulting action describes a pair of non-linear O(3) nonlinear sigma models interacting with a scalar field. The potential of the scalar field is a Mexican hat and the location of the minima sets the energy scale of solitonic configurations of the sigma model fields whose excitations correspond to glueball states.