Current Exchanges and Unconstrained Higher Spins

TL;DR

This paper explores unconstrained higher-spin gauge theories, developing minimal local formulations, extending them to (A)dS spaces, and clarifying the relationship between local and non-local descriptions through current exchange analysis.

Contribution

It constructs one-parameter families of Lagrangians for unconstrained higher-spin fields, extends these to (A)dS backgrounds, and clarifies the link between local and non-local formulations via current exchanges.

Findings

Established equivalence between constrained and unconstrained local formulations.

Identified non-local Lagrangian equations matching current exchange behavior.

Extended formulations to (A)dS backgrounds.

Abstract

The (Fang-)Fronsdal formulation for free fully symmetric (spinor-) tensors rests on (gamma-)trace constraints on gauge fields and parameters. When these are relaxed, glimpses of the underlying geometry emerge: the field equations extend to non-local expressions involving the higher-spin curvatures, and with only a pair of additional fields an equivalent ``minimal'' local formulation is also possible. In this paper we complete the discussion of the ``minimal'' formulation for fully symmetric (spinor-) tensors, constructing one-parameter families of Lagrangians and extending them to (A)dS backgrounds. We then turn on external currents, that in this setting are subject to conventional conservation laws and, by a close scrutiny of current exchanges in the various formulations, we clarify the precise link between the local and non-local versions of the theory. To this end, we first show the equivalence of the constrained and unconstrained local formulations, and then identify a unique set of non-local Lagrangian equations which behave in exactly the same fashion in current exchanges.