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 \( \overline{\mathrm{MHV}} \) 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.
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Adamo, T., Hähnel, P. & McLoughlin, T. Conformal higher spin scattering amplitudes from twistor space. J. High Energ. Phys. 2017, 21 (2017). https://doi.org/10.1007/JHEP04(2017)021
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DOI: https://doi.org/10.1007/JHEP04(2017)021