Nonrenormalization and naturalness in a class of scalar-tensor theories

Claudia De Rham, Gregory Gabadadze, Lavinia Heisenberg, David Pirtskhalava

    Research output: Contribution to journalArticle

    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 languageEnglish (US)
    Article number085017
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Volume87
    Issue number8
    DOIs
    StatePublished - Apr 10 2013

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    gravitons
    tensors
    scalars
    operators
    ghosts
    perturbation theory
    gravitation
    energy
    symmetry
    estimates
    interactions

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics

    Cite this

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

    In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 87, No. 8, 085017, 10.04.2013.

    Research output: Contribution to journalArticle

    De Rham, Claudia ; Gabadadze, Gregory ; Heisenberg, Lavinia ; Pirtskhalava, David. / Nonrenormalization and naturalness in a class of scalar-tensor theories. In: Physical Review D - Particles, Fields, Gravitation and Cosmology. 2013 ; Vol. 87, No. 8.
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