Chiral Higher Spin Theories and Self-Duality

TL;DR

This work shows that chiral higher spin theories in four-dimensional flat space can be understood as generalized self-dual Yang–Mills theories governed by gauge algebras derived from their cubic vertices. The authors construct these algebras, relate the equations of motion to self-duality conditions, and demonstrate infinite hidden symmetries that imply integrability. They also reveal that off-shell amplitudes satisfy generalized BCJ relations with kinematic factors linked to the corresponding self-dual theories, and propose generalized double-copy constructions across higher-spin sectors. A universal Lorentz-invariance argument via light-cone deformations explains the Jacobi identities for these algebras, and the paper catalogues various subalgebras, contractions (including Poisson-type), and degenerate cases. Collectively, the results illuminate a unifying algebraic and geometric framework for chiral higher spin interactions and point toward potential parity-invariant completions and connections to twistor theory and string-inspired formalisms, while acknowledging locality challenges in flat space.

Abstract

We study recently proposed chiral higher spin theories - cubic theories of interacting massless higher spin fields in four-dimensional flat space. We show that they are naturally associated with gauge algebras, which manifest themselves in several related ways. Firstly, the chiral higher spin equations of motion can be reformulated as the self-dual Yang-Mills equations with the associated gauge algebras instead of the usual colour gauge algebra. We also demonstrate that the chiral higher spin field equations, similarly to the self-dual Yang-Mills equations, feature an infinite algebra of hidden symmetries, which ensures their integrability. Secondly, we show that off-shell amplitudes in chiral higher spin theories satisfy the generalised BCJ relations with the usual colour structure constants replaced by the structure constants of higher spin gauge algebras. We also propose generalised double copy procedures featuring higher spin theory amplitudes. Finally, using the light-cone deformation procedure we prove that the structure of the Lagrangian that leads to all these properties is universal and follows from Lorentz invariance.