Twistor space observables and quasi-amplitudes in 4D higher-spin gravity

Vasiliev equations facilitate globally defined formulations of higher-spin gravity in various correspondence spaces associated with different phases of the theory. In the four-dimensional case this induces a correspondence between a generally covariant formulation in spacetime with higher-derivative interactions to a formulation in terms of a deformed symplectic structure on a noncommutative doubled twistor space, whereby spacetime boundary conditions correspond to sectors of an associative star-product algebra. In this paper, we look at obseryables given by integrals over twistor space defining composite zero-forms in spacetime that do not break any local symmetries and that are closed on shell. They are nonlocal observables that can be evaluated in single coordinate charts in spacetime and interpreted as building blocks for dual amplitudes. To regularize potential divergencies arising in their curvature expansion from integration over twistor space, we propose a closed-contour prescription that respects associativity and hence higher-spin gauge symmetry. Applying this regularization scheme to twistor-space plane waves, we show that there exists a class of dual amplitudes given by supertraces. In particular, we examine next-to-leading corrections, and find cancellations that we interpret using transgression properties in twistor space.