Massless chiral fields in six dimensions

TL;DR

This work formulates massless chiral higher-spin fields in six dimensions as a pair of fields, a 0-form $\Psi^{A(2s)}$ and a gauge 2-form $\omega_{A(2s-2)}{}^B$, taking values in totally symmetric $SU^*(4)$ tensors and organized by rectangular Young diagrams. It shows that free dynamics can be encoded in first-order equations and an action, and that a simple interacting deformation couples a tower of singletons to a background $\mathfrak{g}$-valued higher-spin connection via a YM-like term plus a BF coupling, with a further cubic deformation governed by a 3-cocycle of $\mathfrak{g}$. The paper then extends the construction to arbitrary even dimensions $d=2r$, preserving the same field-content pattern and yielding pairs of singletons with chiralities determined by $r$, and discusses current-type interactions and a potential partially-massless extension. Together, these results provide a concrete, gauge-invariant framework for 6d chiral higher-spin fields, connect to higher-form symmetries, and offer a pathway to higher-dimensional generalizations and twistor-inspired formulations.

Abstract

Massless chiral fields of arbitrary spin in six spacetime dimensions, also known as higher spin singletons, admit a simple formulation in terms of $SU^*(4) \cong SL(2,\mathbb{H})$ tensors. We show that, paralleling the four-dimensional case, these fields can be described using a $0$-form and a gauge $2$-form, taking values in totally symmetric tensors of $SU^*(4)$. We then exhibit an example of interacting theory that couples a tower of singletons of all integer spin to a background of $\mathfrak{g}$-valued higher spin fields, for $\mathfrak{g}$ an arbitrary Lie algebra equipped with an invariant symmetric bilinear form. Finally, we discuss the formulation of these models in arbitrary even dimensions, as well as their partially-massless counterpart.