Massless chiral fields in six 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 $S{U}^{\ast }(4)\cong SL(2,\mathbb{H})$ 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 $S{U}^{\ast }(4)$. 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.

v2: A few typos corrected, clarification of the reducibility of gauge symmetries and additional comments on current interactions

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