Conformal Higher Spin Theory and Twistor Space Actions

Abstract

We consider the twistor description of conformal higher spin theories and give twistor space actions for the self-dual sector of theories with spin greater than two that produce the correct flat space-time spectrum. We identify a ghost-free subsector, analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, which generates the unique spin-s three-point anti-MHV amplitude consistent with Poincare invariance and helicity constraints. By including interactions between the infinite tower of higher-spin fields we give a geometric interpretation to the twistor equations of motion as the integrability condition for a holomorphic structure on an infinite jet bundle. Finally, we introduce anti-self-dual interaction terms to define a twistor action for the full conformal higher spin theory.

30 pages + 7 pages appendix and references

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Cited by in corpus (17)

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• Basic introduction to higher-spin theories
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• Twistor Constructions for Higher-spin Extensions of (Self-dual) Yang-Mills
• Toward a twistor action for chiral higher-spin gravity
• Higher-Spin Self-Dual Yang-Mills and Gravity from the twistor space
• Chiral Higher Spin Gravity and Convex Geometry
• A Twistorial Description of the IKKT-Matrix Model
• Self-dual Gravitational Instantons in Conformal Gravity: Conserved Charges and Thermodynamics
• Presymplectic BV-AKSZ formulation of Conformal Gravity
• Twistor fishnets
• Constraining higher-spin S-matrices
• Infinite distances in multicritical CFTs and higher-spin holography
• Scattering amplitudes as multi-particle higher-spin charges in the correspondence space
• Chiral Higher Spin Gravity in (A)dS${}_4$ and secrets of Chern-Simons Matter Theories