The single copy of the gravitational holonomy

TL;DR

This paper introduces a novel concept of a single copy gravitational holonomy, distinguishing it from gauge theory holonomy, and explores its properties and implications for extending the classical double copy framework.

Contribution

It defines a new single copy gravitational holonomy, analyzes its properties, and clarifies misconceptions about gravitational Wilson lines and holonomy.

Findings

Single copy gravitational holonomy differs from gauge theory holonomy.

Examples show cases of reduced holonomy groups.

Results may extend the classical double copy framework.

Abstract

The double copy is a well-established relationship between gravity and gauge theories. It relates perturbative scattering amplitudes as well as classical solutions, and recently there has been mounting evidence that it also applies to non-perturbative information. In this paper, we consider the holonomy properties of manifolds in gravity and prescribe a single copy of gravitational holonomy that differs from the holonomy in gauge theory. We discuss specific cases and give examples where the single copy holonomy group is reduced. Our results may prove useful in extending the classical double copy. We also clarify previous misconceptions in the literature regarding gravitational Wilson lines and holonomy.