Maxwell-like Lagrangians for higher spins

TL;DR

The paper develops Maxwell-like Lagrangians for massless bosons of arbitrary spin by enforcing divergence-free gauge invariance, yielding a simple kinetic operator structure analogous to Maxwell theory. It extends the construction to flat and (A)dS backgrounds and to tensors of mixed symmetry, distinguishing irreducible and reducible spectra via trace constraints and recovering tensionless-string triplet content in unconstrained cases. Symmetric-tensor cases admit clean AdS deformations with spin-dependent mass terms and preserved gauge symmetry; mixed-symmetry cases require additional constraints and, in AdS, Stueckelberg-type extensions to realize unitary multiplets, consistent with the BMV pattern. The reducible theories can be diagonalised into sums of single-particle Lagrangians in both flat and AdS spaces, providing ghost-free, tractable decompositions and clarifying the particle content and its relation to tensionless strings, with several important open questions remaining for fully unconstrained AdS mixed-symmetry theories and interactions.

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.