Minimal Local Lagrangians for Higher-Spin Geometry

TL;DR

This paper introduces minimal local Lagrangians for higher-spin fields that incorporate compensator and Lagrange multiplier fields, enabling derivation of geometric equations without trace constraints on gauge parameters.

Contribution

It presents a simplified local Lagrangian formulation for higher-spin geometry using only two additional fields, removing the need for trace constraints.

Findings

Local Lagrangians recover geometric equations

Two additional fields suffice for unconstrained higher-spin fields

Applicable to both bosonic and fermionic higher-spin tensors

Abstract

The Fronsdal Lagrangians for free totally symmetric rank-s tensors rest on suitable trace constraints for their gauge parameters and gauge fields. Only when these constraints are removed, however, the resulting equations reflect the expected free higher-spin geometry. We show that geometric equations, in both their local and non-local forms, can be simply recovered from local Lagrangians with only two additional fields, a rank-(s-3) compensator and a rank-(s-4) Lagrange multiplier. In a similar fashion, we show that geometric equations for unconstrained rank-n totally symmetric spinor-tensors can be simply recovered from local Lagrangians with only two additional spinor-tensors, a rank-(n-2) compensator and a rank-(n-3) Lagrange multiplier.