On the FP-ghost propagators for Yang-Mills theories and perturbative quantum gravity in the covariant gauge in de Sitter spacetime

TL;DR

This paper addresses IR divergences in FP-ghost propagators in de Sitter spacetime for Yang-Mills and quantum gravity, proposing a regularization method that removes problematic modes without affecting physical calculations.

Contribution

It introduces a regularization scheme for IR divergences in FP-ghost propagators by removing modes responsible for divergences, applicable to Yang-Mills and quantum gravity in de Sitter space.

Findings

Proposed effective FP-ghost propagators free of IR divergences.

Showed that divergent modes do not contribute to loop diagrams.

Commented on similar issues in anti-de Sitter spacetime.

Abstract

The propagators of the Faddeev-Popov (FP) ghosts for Yang-Mills theories and perturbative quantum gravity in the covariant gauge are infrared (IR) divergent in de Sitter spacetime. We point out, however, that the modes responsible for these divergences will not contribute to loop diagrams in computations of time-ordered products in either Yang-Mills theories or perturbative quantum gravity. Therefore we propose that the IR divergent FP-ghost propagator should be regularized by a small mass term that is sent to zero in the end of any perturbative calculations. This proposal is equivalent to using the effective FP-ghost propagators, which we present in an explicit form, obtained by removing the modes responsible for the IR divergences. We also make some comments on the corresponding propagators in anti-de Sitter spacetime.