Abstract
The double copy is a map from non-abelian gauge theories to gravity, that has been demonstrated both for scattering amplitudes and exact classical solutions. In this study, we reconsider the double copy for exact solutions that are self-dual in either the gauge or gravity theory. In this case, one may formulate a general double copy in terms of a certain differential operator, which generates the gauge and gravity solutions from a harmonic function residing in a biadjoint scalar theory. As an illustration, we examine the single copy of the well-known Eguchi-Hanson instanton in gravity. The gauge field thus obtained represents an abelian-like object whose field is dipole-like at large distances, and which has no magnetic or electric charge.
Highlights
JHEP01(2019)107 for identifying linearised fields in a wide variety of exotic theories, and in a gauge-invariant manner
The first paper to explore the double copy of exact classical solutions [44] pointed out that the properties of self-dual amplitudes can be recast in a KerrSchild language, but where the null vectors are interpreted as differential operators
We have examined the double copy for exact classical solutions of gauge theory and gravity that are Kerr-Schild, and self-dual
Summary
We briefly review the properties of the Kerr-Schild double copy, including its formulation tailored to self-dual solutions. The metric gμν is of Kerr-Schild form if the graviton field can be written as hμν = Φ kμ kν ,. In gauge theory and gravity respectively, where Fμν (Rμνλσ) is the field strength tensor (Riemann curvature), and μνρσ the Levi-Cevita symbol Such solutions correspond to keeping only one of the two physical polarisation states of the photon or graviton, and for such solutions one may think about the Kerr-Schild double copy in a different way. Equation (2.14) is the Plebanski equation describing self-dual gravity, and a similar equation can be obtained for Yang-Mills theory by considering the Kerr-Schild single copy field. For an adjoint-valued scalar field Φ = ΦaTa, where Ta is a generator of the gauge group With this ansatz, the Yang-Mills equations turn out to imply. Having set up the general framework for self-dual classical solutions, we consider a particular example in detail
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