Compact space and infrared behavior of the effective QCD

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 behavior 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. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The study investigates the infrared regime of the new quadratic gauge effective theory in the physical compact space defined on a 4-sphere. Abelian dominance is observed with off-diagonal gluons acquiring mass that is position dependent due to the curved geometry of the 4-sphere. The effective action in the confined phase on the 4-sphere is found to be equivalent to that in 4-dimensional Euclidean space.