Geometric massive higher spins and current exchanges

TL;DR

This work develops a geometric, auxiliary-field‑free framework for massive higher‑spin fields in flat space by introducing generalized Fierz–Pauli mass terms $M_{\varphi}$ that deform the massless divergenceless tensor sector. The mass terms are uniquely fixed by requiring the divergence of the equations of motion to reproduce the Fierz–Pauli constraint, which yields a universal expansion of $M_{\varphi}$ as a series of traces with specific coefficients, ensuring irreducible propagation and on‑shell consistency $(\Box - m^{2})\varphi=0$. The authors compute the massive propagator and its current exchange with conserved external sources, showing that the exchange structure is entirely encoded in $M_{\varphi}$ and matches results from KK reductions and prior unconstrained formulations. The results support a minimal, geometrical description of massive higher‑spin interactions and point toward extensions to (A)dS backgrounds, with a clear link between current exchange and the mass term.

Abstract

Generalised Fierz-Pauli mass terms allow to describe massive higher-spin fields on flat background by means of simple quadratic deformations of the corresponding geometric, massless Lagrangians. In this framework there is no need for auxiliary fields. We briefly review the construction in the bosonic case and study the interaction of these massive fields with external sources, computing the corresponding propagators. In the same fashion as for the massive graviton, but differently from theories where auxiliary fields are present, the structure of the current exchange is completely determined by the form of the mass term itself.