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

TL;DR

This paper explores twistor space observables in 4D higher spin gravity, proposing a regularization method and analyzing corrections to quasi-amplitudes, revealing symmetry-preserving cancellations.

Contribution

It introduces a twistor space integral framework for higher-spin observables and a regularization scheme that maintains gauge symmetry.

Findings

Regularization preserves higher-spin gauge symmetry.

Next-to-leading corrections show cancellations.

Observables serve as building blocks for dual 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.