Cubic vertices of arbitrary-spin massless fields in lightcone gauge are expressed as direct generalizations of abelian vertices built from linearized curvatures, yielding consistency of self-dual theories in (A)dS with no higher vertices needed.
Quantum Chiral Higher Spin Gravity
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abstract
An example of a higher spin gravity in four-dimensional flat space has recently been constructed in arXiv:1609.04655 [hep-th]. This theory is chiral and the action is written in the light-cone gauge. The theory has certain stringy features, e.g. admits Chan-Paton factors. We show that the theory is consistent, both at the classical and quantum level. Even though the interactions are non-trivial, due to the coupling conspiracy all tree level amplitudes vanish on-shell. The loop corrections also vanish. Therefore, the full quantum S-matrix is one and the theory is consistent with the numerous no-go theorems. This provides the first example of a (quantum) interacting higher spin gravity with an action. We argue that higher spin gravities in AdS space should display the same features.
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All self-dual theories with or without higher-spin fields possess nontrivial tree-level amplitudes in Kleinian or complex Minkowski kinematics, completing the celestial analogue of the higher-spin duality.
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Universal structure in the interactions of massless fields on the lightcone
Cubic vertices of arbitrary-spin massless fields in lightcone gauge are expressed as direct generalizations of abelian vertices built from linearized curvatures, yielding consistency of self-dual theories in (A)dS with no higher vertices needed.
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Amplitudes in self-dual (higher-spin) theories
All self-dual theories with or without higher-spin fields possess nontrivial tree-level amplitudes in Kleinian or complex Minkowski kinematics, completing the celestial analogue of the higher-spin duality.