Compact space and infrared behavior of the effective QCD

TL;DR

This paper investigates the infrared behavior of an effective quadratic gauge theory in a compact 4-sphere, revealing Abelian dominance and position-dependent gluon masses due to curvature, with implications for confinement.

Contribution

It demonstrates Abelian dominance and gluon mass behavior in a compact space, showing the curvature's effect on infrared properties and equivalence of effective actions in different geometries.

Findings

Abelian dominance observed in ghost condensed vacuum on 4-sphere

Gluon mass becomes position dependent due to curvature

Effective action in confined phase is identical in 4-sphere and Euclidean space

Abstract

We aim to investigate the infrared regime in the effective theory of the new quadratic gauge in the physical compact space by defining it on 4-sphere. Abelian dominance is characterized by off-diagonal gluons acquiring dynamical masses and it hints at existence of confinement. We do observe Abelian dominance in the ghost condensed vacuum of this theory on 4-sphere. Along with this observation, we find an unusual result that mass of an off-diagonal gluon on 4-sphere is position dependent in this theory as a consequence of the curved geometry. This suggests that the curvature of 4-sphere does not change the infrared behaviour of present theory on 4-sphere from that of the theory with the same quadratic gauge in Euclidean spacetime as Abelian dominance is observed in Euclidean spacetime too while it has caused mass of an off-diagonal gluon on 4-sphere to be position dependent. The effective action in the confined phase on 4-sphere and that in the 4-dim Euclidean space are found to be identical in a profound outcome.