### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 334-338 |

Number of pages | 5 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 693 |

Issue number | 3 |

DOIs | |

State | Published - Oct 2010 |

### Fingerprint

### Keywords

- Massive gravity
- Nonlinear stability

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,

*693*(3), 334-338. https://doi.org/10.1016/j.physletb.2010.08.043

**Selftuned massive spin-2.** / de Rham, Claudia; Gabadadze, Gregory.

Research output: Contribution to journal › Article

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*, vol. 693, no. 3, pp. 334-338. https://doi.org/10.1016/j.physletb.2010.08.043

}

TY - JOUR

T1 - Selftuned massive spin-2

AU - de Rham, Claudia

AU - Gabadadze, Gregory

PY - 2010/10

Y1 - 2010/10

N2 - 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.

AB - 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.

KW - Massive gravity

KW - Nonlinear stability

UR - http://www.scopus.com/inward/record.url?scp=77956874725&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956874725&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2010.08.043

DO - 10.1016/j.physletb.2010.08.043

M3 - Article

VL - 693

SP - 334

EP - 338

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 3

ER -