Weyl double copy and massless free-fields in curved spacetimes

Abstract

In spinor formalism, since any massless free-field spinor with spin higher than 1/2 can be constructed with spin-1/2 spinors (Dirac-Weyl spinors) and scalars, we introduce a map between Weyl fields and Dirac-Weyl fields. We determine the corresponding Dirac- Weyl spinors in a given empty spacetime. Regarding them as basic units, other higher spin massless free-field spinors are then identified. Along this way, we find some hidden fundamental features related to these fields. In particular, for non-twisting vacuum Petrov type N solutions, we show that all higher spin massless free-field spinors can be constructed with one type of Dirac-Weyl spinor and the zeroth copy. Furthermore, we systematically rebuild the Weyl double copy for non-twisting vacuum type N and vacuum type D solutions. Moreover, we show that the zeroth copy not only connects the gravity fields with a single copy but also connects the degenerate Maxwell fields with the Dirac-Weyl fields in the curved spacetime, both for type N and type D cases. Besides, we extend the study to non- twisting vacuum type III solutions. We find a particular Dirac-Weyl scalar independent of the proposed map and whose square is proportional to the Weyl scalar. A degenerate Maxwell field and an auxiliary scalar field are then identified. Both of them play similar roles as the Weyl double copy. The result further inspires us that there is a deep connection between gravity theory and gauge theory.

Aligned fields double copy to Kerr-NUT-(A)dS

“…In the Weyl double copy, a single copy field strength and zeroth copy scalar are proposed which combine to form the Weyl tensor directly. Following the first proposal for Petrov type D spacetimes in [39], the Weyl double copy was extended to other Petrov types [40] and has found justification from amplitudes directly [41][42][43][44][45][46][47][48][49]. Aside from the spinor formalism (extended to five dimensions in [7]), we additionally verify our five-dimensional copy via the Weyl doubling formula of [50].…”

Einstein-Maxwell theory and the Weyl double copy

“…Alternately, imposing the (sourced) Weyl double copy in double-field theory could be provide a mechanism to study the relation between T duality and double copy for type-D solutions. 16 Further, it would be interesting to extend our current analysis to other types of black hole spacetimes, particularly those including a cosmological constant (whose Weyl double copy was presented in [57]), additional Abelian gauge fields [58], and massless or higher-spin fields [59,60]. It would also be interesting to adapt our formalism to threedimensional spacetimes, such as the Bañados-Teitelboim-Zanelli (BTZ) black hole [61], its quantum and de Sitter generalizations [62,63], or generalized three-dimensional solutions described in [64,65].…”

A spinorial double copy for ${\cal N}=0$ supergravity

“…(33)(34)(35)(36) constitute the fact that classical spinor fields in N = 0 supergravity at linearised level can be expressed in terms of on-shell inverse Fourier transforms of three-point amplitudes, where the latter are obtained by double-copying gauge theory amplitudes according to eq. (32). Reference [90] used these formulae as a starting point for examining whether or not one may formulate exact position-space double copies for particular solutions, after converting all spinor fields into the tensorial language.…”