Conformal higher spin scattering amplitudes from twistor space

TL;DR

This paper explores conformal higher spin theories in twistor space, deriving scattering amplitudes and analyzing their properties, including the triviality of the S-matrix in the unitary sector and connections to chiral higher spin theories.

Contribution

It provides explicit formulas for tree-level scattering amplitudes of conformal higher spins in twistor space and investigates their behavior in the flat-space limit.

Findings

All three-point anti-MHV amplitudes derived.

Amplitudes involving positive helicity conformal gravity and negative higher spins obtained.

In the unitary sector, the S-matrix vanishes in flat space, but rescaling yields non-trivial results.

Abstract

We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point anti-MHV amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins. This provides the on-shell analogue for the covariant coupling of CHS fields to a conformal gravity background. We discuss the restriction of the theory to a ghost-free unitary subsector, analogous to restricting conformal gravity to general relativity with a cosmological constant. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of CHS theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories.