Higher-Spin Geometry and String Theory

TL;DR

This work presents an unconstrained formulation of free massless higher-spin fields that removes trace constraints by introducing a pair of auxiliary fields, yielding local Lagrangians that are gauge invariant under unconstrained transformations and reduce to the Fronsdal system via partial gauge fixing. It shows that eliminating the auxiliary fields leads to a non-local, geometric description in which higher-spin curvatures acquire dynamical meaning akin to generalized Maxwell and Einstein equations, and builds a detailed link between these formulations and the low-tension limit of String Field Theory via triplet systems. The authors further relate the unconstrained framework to the Vasiliev equations, arguing that compensator fields emerge as exact forms within a cohomological picture, and discuss the implications for a possible off-shell, metric-like geometry underlying higher-spin interactions. Overall, the paper advances the understanding of higher-spin geometry by unifying local compensator approaches, non-local geometric formulations, string-theoretic connections, and the constraint structure of Vasiliev theory. These insights pave the way for a more coherent picture of higher-spin dynamics and their role in string theory and gravitational contexts.

Abstract

The theory of freely-propagating massless higher spins is usually formulated via gauge fields and parameters subject to trace constraints. We summarize a proposal allowing to forego them by introducing only a pair of additional fields in the Lagrangians. In this setting, external currents satisfy usual Noether-like conservation laws, the field equations can be nicely related to those emerging from Open String Field Theory in the low-tension limit, and if the additional fields are eliminated without reintroducing the constraints a geometric, non-local description of the theory manifests itself.