We reformulate chiral higher-spin Yang-Mills and gravity on R⁴ 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 S⁷, S³ R⁴ or AdS₃+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 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.
Mason et al. (Wed,) studied this question.
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