Generalization of the Fierz-Pauli Action

TL;DR

This work studies the most general covariant polynomial potential for a massive spin-2 field in 4D flat space, aiming to avoid the Boulware-Deser ghost within the decoupling limit. By tuning higher-order interaction coefficients, it demonstrates ghost-free behavior up to quintic order and reveals that the helicity-0 mode naturally generates Galileon-type interactions at the scale Λ3, with mixing to the helicity-2 mode constrained to quartic order in the decoupling limit. Through a structured redefinition and careful conservation properties of the interaction tensors, the authors connect the decoupling-limit dynamics to the Galileon family, while clarifying the limitations of extrapolating these results away from the decoupling limit. The findings suggest a consistent EFT below Λ3 and motivate further nonperturbative or higher-dimensional constructions to address potential BD ghosts beyond the decoupling regime and to assess quantum stability.

Abstract

We consider the Lagrangian of gravity covariantly amended by the mass and polynomial interaction terms with arbitrary coefficients, and reinvestigate the consistency of such a theory in the decoupling limit, up to the fifth order in the nonlinearities. We calculate explicitly the self-interactions of the helicity-0 mode, as well as the nonlinear mixing between the helicity-0 and -2 modes. We show that ghost-like pathologies in these interactions disappear for special choices of the polynomial interactions, and argue that this result remains true to all orders in the decoupling limit. Moreover, we show that the linear, and some of the nonlinear mixing terms between the helicity-0 and -2 modes can be absorbed by a local change of variables, which then naturally generates the cubic, quartic, and quintic Galileon interactions, introduced in a different context. We also point out that the mixing between the helicity-0 and 2 modes can be at most quartic in the decoupling limit. Finally, we discuss the implications of our findings for the consistency of the effective field theory away from the decoupling limit, and for the Boulware-Deser problem.