Higher spin fields and the field strength multicopy

Abstract

We discuss the generalisation of the Weyl double copy to higher spin "multi-copies", showing how the natural linearised higher spin field strengths can be related to sums of powers of the Maxwell tensor. The tracelessness of the field strength involves the appropriate Fronsdal equations of motion for the higher spin field. We work with spacetimes admitting Kerr-Schild coordinates and give a number of examples in different dimensions. We note that the multi-copy is particularly transparent in four dimensions if one uses spinor descriptions of the fields, relating this to the Penrose transform. The higher-dimensional spinor multicopy is also explored and reveals some interesting new features arising from the little group based identification of higher spin field strengths and Maxwell tensor types. We then turn to the vector superspace formalism describing higher spin and `continuous' spin representations given by Schuster and Toro, based on symmetric tensor fields. Here the Kerr-Schild higher spin fields we have used earlier naturally package into a simple expression involving an arbitrary function, when the continuous spin scale $ρ$ is set to zero. Further, we discuss the case of an anti-de Sitter background, where there is also a vector space formalism given by Segal and we clarify this approach using a different definition of the covariant derivative. We give a general solution of Kerr-Schild type and finally we describe some of the obstacles to a continuous spin formulation.