Gravitationally induced zero modes of the Faddeev-Popov operator in the Coulomb gauge for Abelian gauge theories

TL;DR

This paper investigates how curved spacetime backgrounds can induce zero modes in the Coulomb gauge Faddeev-Popov operator for Abelian gauge theories, revealing challenges in gauge fixing and implications for quantum field theory.

Contribution

It provides a detailed analysis of zero modes in curved backgrounds, deriving conditions and explicit metric expressions, especially for static spherically symmetric spacetimes.

Findings

Zero modes can exist in the Coulomb gauge on curved backgrounds even for Abelian theories.

Explicit metric conditions for zero modes are derived for static spherically symmetric spacetimes.

The analysis includes the asymptotic behavior of metrics like Anti de-Sitter space that induce zero modes.

Abstract

It is shown that on curved backgrounds, the Coulomb gauge Faddeev-Popov operator can have zero modes even in the abelian case. These zero modes cannot be eliminated by restricting the path integral over a certain region in the space of gauge potentials. The conditions for the existence of these zero modes are studied for static spherically symmetric spacetimes in arbitrary dimensions. For this class of metrics, the general analytic expression of the metric components in terms of the zero modes is constructed. Such expression allows to find the asymptotic behavior of background metrics, which induce zero modes in the Coulomb gauge, an interesting example being the three dimensional Anti de-Sitter spacetime. Some of the implications for quantum field theory on curved spacetimes are discussed.