Study of Abelian dominance in Sp(N) QCD in the de Sitter background

Abstract

We propose the effective theory based on the compact symplectic group Sp(N) in the new quadratic gauge on the 4-dimensional de Sitter spacetime (dS 4) with a view to investigate the infrared regime in it. 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 in the de Sitter background. Along with this observation, we find an unusual result that the mass of an off-diagonal gluon on dS 4 is position dependent as a consequence of the curved geometry. In our previous papers, we have shown that Abelian dominance is strongly indicated in the Minkowski spacetime too. Therefore, the present observation suggests that the curvature of the dS 4 does not change the infrared behaviour of the present theory on dS 4 from that of the quadratic gauge fixed theory in Minkowski spacetime, but it causes the mass of an off-diagonal gluon on the dS 4 to be position dependent.