### Abstract

We study the renormalization of some dimension-4, 7 and 10 operators in a class of nonlinear scalar-tensor theories. These theories are invariant under (a) linear diffeomorphisms which represent an exact symmetry of the full nonlinear action, and (b) global field-space Galilean transformations of the scalar field. The Lagrangian contains a set of nontopological interaction terms of the above-mentioned dimensionality, which we show are not renormalized at any order in perturbation theory. We also discuss the renormalization of other operators, that may be generated by loops and/or receive loop corrections, and identify the regime in which they are subleading with respect to the operators that do not get renormalized. Interestingly, such scalar-tensor theories emerge in a certain high-energy limit of the ghost-free theory of massive gravity. One can use the nonrenormalization properties of the high-energy limit to estimate the magnitude of quantum corrections in the full theory. We show that the quantum corrections to the three free parameters of the model, one of them being the graviton mass, are strongly suppressed. In particular, we show that having an arbitrarily small graviton mass is technically natural.

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

Article number | 085017 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 87 |

Issue number | 8 |

DOIs | |

State | Published - Apr 10 2013 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*87*(8), [085017]. https://doi.org/10.1103/PhysRevD.87.085017

**Nonrenormalization and naturalness in a class of scalar-tensor theories.** / De Rham, Claudia; Gabadadze, Gregory; Heisenberg, Lavinia; Pirtskhalava, David.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 87, no. 8, 085017. https://doi.org/10.1103/PhysRevD.87.085017

}

TY - JOUR

T1 - Nonrenormalization and naturalness in a class of scalar-tensor theories

AU - De Rham, Claudia

AU - Gabadadze, Gregory

AU - Heisenberg, Lavinia

AU - Pirtskhalava, David

PY - 2013/4/10

Y1 - 2013/4/10

N2 - We study the renormalization of some dimension-4, 7 and 10 operators in a class of nonlinear scalar-tensor theories. These theories are invariant under (a) linear diffeomorphisms which represent an exact symmetry of the full nonlinear action, and (b) global field-space Galilean transformations of the scalar field. The Lagrangian contains a set of nontopological interaction terms of the above-mentioned dimensionality, which we show are not renormalized at any order in perturbation theory. We also discuss the renormalization of other operators, that may be generated by loops and/or receive loop corrections, and identify the regime in which they are subleading with respect to the operators that do not get renormalized. Interestingly, such scalar-tensor theories emerge in a certain high-energy limit of the ghost-free theory of massive gravity. One can use the nonrenormalization properties of the high-energy limit to estimate the magnitude of quantum corrections in the full theory. We show that the quantum corrections to the three free parameters of the model, one of them being the graviton mass, are strongly suppressed. In particular, we show that having an arbitrarily small graviton mass is technically natural.

AB - We study the renormalization of some dimension-4, 7 and 10 operators in a class of nonlinear scalar-tensor theories. These theories are invariant under (a) linear diffeomorphisms which represent an exact symmetry of the full nonlinear action, and (b) global field-space Galilean transformations of the scalar field. The Lagrangian contains a set of nontopological interaction terms of the above-mentioned dimensionality, which we show are not renormalized at any order in perturbation theory. We also discuss the renormalization of other operators, that may be generated by loops and/or receive loop corrections, and identify the regime in which they are subleading with respect to the operators that do not get renormalized. Interestingly, such scalar-tensor theories emerge in a certain high-energy limit of the ghost-free theory of massive gravity. One can use the nonrenormalization properties of the high-energy limit to estimate the magnitude of quantum corrections in the full theory. We show that the quantum corrections to the three free parameters of the model, one of them being the graviton mass, are strongly suppressed. In particular, we show that having an arbitrarily small graviton mass is technically natural.

UR - http://www.scopus.com/inward/record.url?scp=84876196818&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876196818&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.87.085017

DO - 10.1103/PhysRevD.87.085017

M3 - Article

AN - SCOPUS:84876196818

VL - 87

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 8

M1 - 085017

ER -