Non-Renormalization and Naturalness in a Class of Scalar-Tensor Theories

TL;DR

This paper demonstrates that certain operators in scalar-tensor theories are not renormalized, and that small graviton mass values are technically natural, with implications for quantum corrections in massive gravity models.

Contribution

The paper proves non-renormalization of specific operators in scalar-tensor theories and links these properties to the naturalness of a small graviton mass in massive gravity.

Findings

Non-renormalization of dimension-4, 7, and 10 operators in the theories.

Quantum corrections to the graviton mass are strongly suppressed.

Small graviton mass is shown to be technically natural.

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 non-linear action, and (b) global field-space Galilean transformations of the scalar field. The Lagrangian contains a set of non-topological 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 sub-leading 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 non-renormalization 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.