Size of the Gribov region in curved spacetime

TL;DR

This paper investigates how spacetime curvature influences the size of the Gribov region, revealing that curvature can cause the Gribov horizon to shift inward or outward, depending on the curvature's sign, through new inequalities.

Contribution

It introduces a simple criterion and novel inequalities to analyze the effect of curvature on the Gribov region's size, improving previous methods.

Findings

The Gribov horizon shifts inward or outward depending on curvature sign.

Derived two new inequalities describing the Gribov region in curved spacetime.

Curvature effects modify infrared Green functions in gauge theories.

Abstract

Recent work in the literature has argued that the joint effect of spacetime curvature and the Gribov ambiguity may introduce further modifications to the Green functions in the infrared. This paper focuses on a simple criterion for studying the effect of spacetime curvature on the size of the Gribov region, improving the accuracy of the previous analysis. It is shown that, depending on the sign of the scalar and Riemann curvature, the Gribov horizon moves inward or, instead, outward with respect to the case of flat spacetime. This is made clear by two novel inequalities here derived for the first time.