Chiral Higher Spin Theories and Self-Duality

TL;DR

This paper explores chiral higher spin theories in four-dimensional flat space, revealing their connection to gauge algebras, integrability via hidden symmetries, and generalizations of BCJ relations and double copy procedures.

Contribution

It demonstrates the gauge algebra structure, integrability, and amplitude relations of chiral higher spin theories, extending known concepts from Yang-Mills to higher spins.

Findings

Chiral higher spin equations are reformulated as self-dual Yang-Mills equations.

Off-shell amplitudes satisfy generalized BCJ relations with higher spin gauge algebra constants.

The Lagrangian structure is shown to be universal and Lorentz invariant.

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.