Hyper-Hermitian Weyl Double Copy

TL;DR

This paper extends the self-dual double copy framework to hyper-Hermitian manifolds using the Weyl double copy formalism, revealing solutions with distinct Maxwell spinors and source properties, thus broadening the understanding of gauge/gravity dualities.

Contribution

It generalizes the hyper-Hermitian double copy to the Weyl formalism and finds explicit solutions with unique Maxwell spinor characteristics.

Findings

Found solutions with two Maxwell spinors, one source-free and one with a source current.

Demonstrated compatibility of hyper-Hermitian spaces with non-Ricci-flat metrics.

Extended the double copy formalism to new classes of hyper-Hermitian geometries.

Abstract

The self-dual double copy is further explored. In previous work, it has been shown that hyper-Hermitian manifolds also have associated the self-dual gauge theories via Kerr-Schild double copy. The self-dual double copy is generalized in the structure of the kinematic algebra by replacing the area-preserving diffeomorphisms algebra with the diffeomorphisms on a surface algebra. This gave rise to the hyper-Hermitian double copy in the Kerr-Schild approach. In the present article, we further study the hyper-Hermitian case using the Weyl double copy formalism. In particular, we have found solutions within this formalism for different hyper-Hermitian metrics. One of the main features is that there will be two Maxwell spinors and one of them is source-free while the other has a source current. This is compatible with the fact that, in general, the hyper-Hermitian spaces are not Ricci-flat.