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.

我们旨在通过在4个球体上定义新的二次规范，在物理紧凑空间的有效理论中研究红外体制。阿贝尔优势地位的特征是非对角线胶子获得动态质量，这暗示了局限性的存在。我们确实在4球体上该理论的幻影浓缩真空中观察到了阿贝尔占主导地位。伴随着这一观察，我们发现了一个不寻常的结果：由于弯曲的几何形状，在此理论中，在4个球面上的非对角胶子的质量与位置有关。这表明4球体的曲率不会改变当前理论在4球体上的红外行为，而与在欧几里德时空中具有二次方规的理论相同，因为在欧几里德时空中也观察到了Abelian优势，尽管它引起了质量的增加。 4球上的非对角胶子取决于位置。发现在有限空间上的4球面上的有效作用和在4维昏暗的欧几里得空间上的有效作用具有相同的深远意义。