Comments on higher-spin symmetries

TL;DR

This paper reviews the unconstrained frame-like formulation of higher-spin gauge fields, explores gauge transformations in the metric-like formulation, and shows their algebraic structure relates to Hermitian differential operators, extending understanding of higher-spin symmetries.

Contribution

It provides a detailed analysis of the gauge symmetry algebra of higher-spin fields in the weak field limit, connecting it to the Lie algebra of Hermitian differential operators.

Findings

Gauge transformations are derived to first order in a weak field expansion.

The gauge algebra is shown to be equivalent to the Lie algebra of Hermitian differential operators.

The algebra reduces to diffeomorphisms in the spin-two sector.

Abstract

The unconstrained frame-like formulation of an infinite tower of completely symmetric tensor gauge fields is reviewed and examined in the limit where the cosmological constant goes to zero. By partially fixing the gauge and solving the torsion constraints, the form of the gauge transformations in the unconstrained metric-like formulation are obtained till first order in a weak field expansion. The algebra of the corresponding gauge symmetries is shown to be equivalent, at this order and modulo (unphysical) gauge parameter redefinitions, to the Lie algebra of Hermitian differential operators on R^n, the restriction of which to the spin-two sector is the Lie algebra of infinitesimal diffeomorphisms.