Amplitudes in self-dual (higher-spin) theories

Abstract: Self-dual theories are powerful toy models of their completions. It was shown recently that there are infinitely many SD-theories once massless higher-spin fields are allowed. The maximal SD-theory is chiral higher-spin gravity. Following the recent [arxiv:2602.12176] we show that all SD-theories, including those with massless higher-spin fields, have nontrivial tree-level amplitudes in Kleinian signature or complex Minkowski kinematics. Within celestial holography, the nontriviality of amplitudes in chiral higher-spin gravity provides the missing ingredient needed to complete the celestial analogue of the vector-model/higher-spin AdS/CFT duality.