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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Self-dual gravity with cosmological constant emerges uniquely as the rigid lower-spin sector of four-dimensional higher-spin interactions when only self-dual vertices are kept.
Topological fields in 4d higher spin theory have a finite number of degrees of freedom and admit a gauge-invariant cubic action for interactions with physical higher spin fields.
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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.
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Self-dual gravity from higher-spin theory
Self-dual gravity with cosmological constant emerges uniquely as the rigid lower-spin sector of four-dimensional higher-spin interactions when only self-dual vertices are kept.
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Topological Fields in $4d$ Higher Spin Theory
Topological fields in 4d higher spin theory have a finite number of degrees of freedom and admit a gauge-invariant cubic action for interactions with physical higher spin fields.