# Stable, finite energy density solutions in the effective theory of non-abelian gauge fields

## TL;DR

This paper derives static solutions in an effective non-Abelian gauge theory that have finite energy density and suggest a natural mass scale related to the gluon condensate, providing insights into the low-energy phase.

## Contribution

It introduces a new class of static solutions in the effective theory of non-Abelian gauge fields with finite energy density and a natural mass scale.

## Key findings

- Solutions are Gaussian in the z component of momentum.
- Solutions are proportional to delta functions of other momentum components.
- Parameters relate to the fourth root of the gluon condensate.

## Abstract

We consider the gauge fixed partition function of pure $SU(N_c)$ gauge theory in axial gauge following the Halpern's field strength formalism. We integrate over $3 (N_c^2-1)$ field strengths using the Bianchi identities and obtain an effective action of the remaining $3 (N_c^2-1)$ field strengths in momentum space. We obtain the static solutions of the equations of motion (EOM) of the effective theory. The solutions exhibit Gaussian nature in the $z$ component of momentum and are proportional to the delta functions of the remaining components of momentum. The solutions render a finite energy density of the system and the parameters are found to be proportional to fourth root of the gluon condensate. It indicates that the solutions offer a natural mass scale in the low energy phase of the theory.