Chiral higher-spin theories from twistor space

TL;DR

This paper reformulates chiral higher-spin theories as CR-holomorphic Chern-Simons theories on twistor space, revealing their structure, spectrum, and vertices, including non-commutative deformations and higher valence interactions.

Contribution

It introduces a novel twistor space formulation of chiral higher-spin theories as CR-holomorphic Chern-Simons models, including non-commutative deformations and analysis of their vertices and spectrum.

Findings

Higher spin fields arise as Kaluza-Klein modes.

Vertices include helicities (+++), (++-), (+--), all of MHV type.

Vertices are supported on anti-self-dual momenta.

Abstract

We reformulate chiral higher-spin Yang-Mills and gravity on $\mathbb{R}^4$ as 'CR-holomorphic' theories of Chern-Simons type; in the most general case, these are Moyal deformed to become non-commutative. They are defined on the space of non-projective twistors of unit length. These spaces carry $S^7$, $S^3\times \mathbb{R}^4$ or AdS$_{3+4}$ metrics but are also endowed with a Cauchy-Riemann structure, an odd-dimensional analogue of a complex structure, with respect to which the theories are holomorphic. They are circle bundles over standard projective twistor spaces and the higher spin fields arise naturally as Kaluza-Klein modes. We give a perturbative analysis to identify the spectrum and three-point vertices on spacetime and, for flat space, in momentum space. These vertices can have helicities $(+++)$, $(++-)$ or $(+--)$, but are nevertheless all of $\overline{\text{MHV}}$ type in the sense that they are supported on momenta with proportional anti-self-dual spinors. On reduction to spacetime, there are higher valence vertices but these appear to be a gauge artifact. Further generalizations are discussed.