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.
Highlights
We have considered the holonomy group in gravity, which consists of the group of transformations acting on vectors that have been parallel transported around a closed curve
The analogue of this in a-abelian gauge theory is the Wilson loop, which has a physical interpretation in terms of the phase experienced by a scalar particle traversing a closed contour
Attempts to match up the physical properties of the holonomy and Wilson line — or to interpret the holonomy operator itself as a gravitational Wilson loop — have been made before [21,22,23,24, 26], with the conclusion that the gravitational holonomy should not be thought as the being the correct physical analogue of the gauge theory Wilson line
Summary
Holonomy refers, in general, to the change in certain mathematical objects as they are transported around a closed loop. We review the relevant ideas that we will need for the rest of the paper
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