Maxwell-like Lagrangians for higher spins

Abstract

We show how implementing invariance under divergence-free gauge transformations leads to a remarkably simple Lagrangian description of massless bosons of any spin. Our construction covers both flat and (A)dS backgrounds and extends to tensors of arbitrary mixed-symmetry type. Irreducible and traceless fields produce single-particle actions, while whenever trace constraints can be dispensed with the resulting Lagrangians display the same reducible, multi-particle spectra as those emerging from the tensionless limit of free open-string field theory. For all explored options the corresponding kinetic operators take essentially the same form as in the spin-one, Maxwell case.

A note on higher-derivative actions for free higher-spin fields

“…coincides with the spin-s tensor of transverse-invariant theories [30,31], defined in terms of Maxwell operator L ,…”

“…We begin with familiar two-derivative constrained formulations of higher-spin fields: Fronsdal's theory [2] and transverse invariant setting of Skvortsov and Vasiliev (SV) [30], recently investigated in a wider context in [31]. Then, increasing the number of derivatives, we identify the Lagrangians compatible with relaxed constraints, and in particular those acquiring Weyl(-like) symmetries.…”

Higher-spin charges in Hamiltonian form. I. Bose fields

“…In AdS they loose almost all gauge symmetries they display in flat space, but the remaining ones should give rise to conserved charges generalising those discussed in this paper. An analysis JHEP10(2016)146 along the lines we followed for symmetric fields may start from the actions of [68], which constitutes at present the closest generalisation of the Fronsdal action known in closed form. Partially massless fields [69][70][71] are other gauge fields which can be defined on constant curvature backgrounds and have less gauge symmetry than Fronsdal's fields.…”

On conformal higher spin wave operators

“…Free Lagrangians and the corresponding wave equations involving massless Fronsdal fields and their variants have received considerable interest [37][38][39][40][41][42][43][44][45][46][47]. But the explicit form of the conformal wave operator for HS fields in curved spaces has not been worked out yet.…”