Selftuned Massive Spin-2

TL;DR

This paper develops a covariant nonlinear theory for massive spin-2 particles, ensuring ghost-free cubic interactions and revealing underlying symmetries that prevent ghost emergence at this order.

Contribution

It introduces a self-tuned, covariant massive spin-2 theory with ghost-free cubic interactions and uncovers potential symmetries responsible for ghost cancellation.

Findings

Cubic terms with six derivatives cancel out automatically.

Ghost-free four-derivative cubic terms for helicity-0 field identified.

Nonlinear redefinitions remove cubic mixing terms, revealing underlying symmetries.

Abstract

We calculate the cubic order terms in a covariant theory that gives a nonlinear completion of the Fierz-Pauli massive spin-2 action. The resulting terms have specially tuned coefficients guarantying the absence of a ghost at this order in the decoupling limit. We show in this limit that: (1) The quadratic theory propagates helicity-2, 1, and helicity-0 states of massive spin-2. (2) The cubic terms with six derivatives -- which would give ghosts on local backgrounds -- cancel out automatically. (3) There is a four-derivative cubic term for the helicity-0 field, that has been known to be ghost-free on any local background. (4) There are four-derivative cubic terms that mix two helicity-0 fields with one helicity-2, or two helicity-1 fields with one helicity-0; none of them give ghosts on local backgrounds. (5) In the absence of external sources, all the cubic mixing terms can be removed by nonlinear redefinitions of the helicity-2 and helicity-1 fields. Notably, the helicity-2 redefinition generates the quartic Galileon term. These findings hint to an underlying nonlinearly realized symmetry, that should be responsible for what appears as the accidental cancellation of the ghost.