On geometric equations and duality for free higher spins

TL;DR

This work clarifies how three distinct formalisms for free higher-spin fields—the local Fronsdal theory, the non-local Francia–Sagnotti construction, and the duality-symmetric curvature approach—are connected through covariant dualisation. By treating curvature tensors as the central objects, the authors derive a unified perspective that naturally yields dual pairs of theories, including a five-dimensional exotic spin-3 gauge field, while preserving the correct degrees of freedom. They provide explicit links between Einstein-like equations, curvature traces, and dual gauge fields for arbitrary spins and mixed-symmetry types, illustrating how duality can generate consistent, covariant descriptions of higher-spin dynamics. The results have implications for geometric formulations of higher-spin theories and potential directions for interactions within duality frameworks.

Abstract

We provide a general scheme for dualizing higher-spin gauge fields in arbitrary irreducible representations of GL(D,R). We also give a recipe for constructing Fronsdal-like field equations and Lagrangians for such exotic fields.