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

TL;DR

This paper develops a framework linking Vasiliev’s four-dimensional higher-spin gravity to a deformed twistor-space formulation, defining locally evaluable zero-form charges that act as building blocks for dual quasi-amplitudes. It introduces a closed-contour (large-contour) regularization in twistor space that preserves associativity and higher-spin gauge symmetry, and applies it to the twistor-plane-wave sector where certain quasi-amplitudes are shown to be protected against next-to-leading corrections. The results reveal cancellations explainable by transgression properties in twistor space, suggesting possible all-order protection in this sector and providing a route toward well-defined, gauge-invariant amplitudes in higher-spin holography. The work lays out a systematic plan to analyze locality, moduli spaces, and holographic interpretations across unfolded HS dynamics, with open questions about extending protection to other sectors and connecting to topological open-string amplitudes.

Abstract

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 map from 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, sending spacetime boundary conditions to various sectors of an associative star-product algebra. We look at observables 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 can be evaluated locally in spacetime and interpreted as building blocks for dual amplitudes. To regularize potential twistor-space divergencies arising in their curvature expansion, we propose a closed-contour prescription that respects associativity and hence higher-spin gauge symmetry. As a sample calculation, we examine next-to-leading corrections to quasi-amplitudes for twistor-space plane waves, and find cancellations that we interpret using transgression properties in twistor space.