Higher-Spin Gauge Fields and Duality

TL;DR

The work develops a geometric framework for free higher-spin gauge fields in $D$ dimensions using a multiform/bi-form calculus that relates covariant $GL(D,\mathbb{R})$ representations to physical $SO(D-2)$ states. It shows how dual formulations arise by exchanging columns in Young tableaux and by dualising field strengths, with gravity serving as a key example. The formalism extends to general $(p_1,\dots,p_N)$-form fields (multi-forms), producing higher-derivative, non-local covariant equations that reduce to local Fronsdal-type equations under gauge fixing, and revealing a rich web of dual descriptions. This provides a comprehensive, gauge-invariant description of higher-spin fields in arbitrary dimensions with potential links to string theory and gravity.

Abstract

We review the construction of free gauge theories for gauge fields in arbitrary representations of the Lorentz group in $D$ dimensions. We describe the multi-form calculus which gives the natural geometric framework for these theories. We also discuss duality transformations that give different field theory representations of the same physical degrees of freedom, and discuss the example of gravity in $D$ dimensions and its dual realisations in detail.