On the relation between local and geometric Lagrangians for higher spins

TL;DR

This paper explores the relationship between local and non-local Lagrangian formulations for free higher-spin gauge fields, proposing a method to derive unique non-local actions from local unconstrained Lagrangians by integrating out auxiliary fields.

Contribution

It introduces a systematic approach to obtain unique non-local higher-spin actions from local unconstrained Lagrangians through functional integration.

Findings

Derivation of non-local actions expressed in terms of curvatures.

Resolution of ambiguities in higher-spin Lagrangian formulations.

Establishment of a connection between local and non-local descriptions.

Abstract

Equations of motion for free higher-spin gauge fields of any symmetry can be formulated in terms of linearised curvatures. On the other hand, gauge invariance alone does not fix the form of the corresponding actions which, in addition, either contain higher derivatives or involve inverse powers of the d'Alembertian operator, thus introducing possible subtleties in degrees of freedom count. We suggest a path to avoid ambiguities, starting from local, unconstrained Lagrangians previously proposed, and integrating out the auxiliary fields from the functional integral, thus generating a unique non-local theory expressed in terms of curvatures.