Massless chiral fields in six dimensions

TL;DR

This paper develops a simple tensor-based formulation for massless chiral fields of arbitrary spin in six dimensions, introduces an interacting model coupling singletons to higher spin backgrounds, and discusses extensions to other even dimensions.

Contribution

It presents a new tensor formulation for higher spin singletons in six dimensions and constructs an interacting theory coupling these to higher spin fields.

Findings

Tensor formulation for 6D massless chiral fields

Example of interacting singleton-higher spin theory

Discussion of models in arbitrary even dimensions

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.