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

TL;DR

This work identifies a non-renormalization property for a class of scalar-tensor theories that arise as the decoupling limit of ghost-free massive gravity. The leading dimension-4,7,10 operators do not renormalize to any order, enabling a technically natural small graviton mass $m$ and a predictive effective field theory below the strong coupling scale $\\Lambda_3=(M_{\\rm Pl} m^2)^{1/3}$. Through DL analysis, the authors bound quantum corrections to $m$ and to the potential parameters, finding strong suppression and preserving IR predictivity; this provides a concrete, non-supersymmetric mechanism for naturalness in infrared gravity and informs potential UV completions and extensions such as quasi-dilaton theories.

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.

Figures (1)

• Figure 1: An arbitrary 1PI diagram with gravitational degrees of freedom in the loop.