Abstract
The Kerr-Schild double copy relates exact solutions of gauge and gravity theories. In all previous examples, the gravity solution is associated with an abelian-like gauge theory object, which linearises the Yang-Mills equations. This appears to be at odds with the double copy for scattering amplitudes, in which the non-abelian nature of the gauge theory plays a crucial role. Furthermore, it is not yet clear whether or not global properties of classical fields — such as non-trivial topology — can be matched between gauge and gravity theories. In this paper, we clarify these issues by explicitly demonstrating how magnetic monopoles associated with arbitrary gauge groups can be double copied to the same solution (the pure NUT metric) in gravity. We further describe how to match up topological information on both sides of the double copy correspondence, independently of the nature of the gauge group. This information is neatly expressed in terms of Wilson line operators, and we argue through specific examples that they provide a useful bridge between the classical double copy and the BCJ double copy for scattering amplitudes.
Highlights
There is, another approach to extending the conceptual framework of the double copy
This information is neatly expressed in terms of Wilson line operators, and we argue through specific examples that they provide a useful bridge between the classical double copy and the BCJ double copy for scattering amplitudes
We have examined the double copy for exact classical solutions, which is normally expressed as a local statement relating the graviton field to products of gauge fields
Summary
The aim of the classical double copy is to associate a given non-abelian gauge theory solution with a gravitational counterpart, in a way that overlaps with the known BCJ double copy for scattering amplitudes where appropriate [1,2,3]. The Kerr-Schild form corresponds to the graviton decomposing into a scalar field φ multiplying an outer product of a vector kμ with itself, where the latter must satisfy null and geodesic properties: ημν kμkν = gμν kμkν = 0, k · ∂kμ = 0 This ansatz turns out to linearise the Einstein equations, such that exact solutions can be more found. Reference [45] analysed this solution in an abelian gauge theory, and concluded that it was a dyon, possessing both electric and magnetic monopole charge These are represented by the first and second terms in eq (2.6) respectively, such that for the case of a pure NUT charge in the gravity theory, one may follow eq (2.4) and write. We discuss how to characterise the non-trivial topology of monopole solutions, in both abelian and non-abelian gauge theories
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