Leading order effective operators in quantum gravity

TL;DR

The study investigates which higher-dimensional operators arise when quantum gravity is treated perturbatively in an EFT framework. It demonstrates that tree-level graviton exchange between SM and hidden-sector fields yields non-local dimension-6 operators, while one-loop graviton effects produce dimension-8 operators, with dimension-5 operators absent in perturbation theory; global symmetries of the tree-level action remain intact at this perturbative level. In the ultralight dark matter context, the gravitationally generated DM–photon couplings are quadratic in the DM field and non-local, implying that linear couplings require UV or non-perturbative gravitational physics. The results constrain how gravity can mediate new interactions in EFTs and have implications for DM phenomenology and the role of Planck-scale fluctuations in symmetry breaking.

Abstract

We explore the nature of higher dimensional operators generated by quantum gravity. Calculating the tree-level and one-loop effective operators generated by graviton exchange between fields of the standard model and those of a hidden sector, we show that the leading order operators generated by quantum gravity are non-local dimension 6 operators. Dimension 5 operators are not generated by perturbative (weak field) effects, although they might be generated by strong field effects such as Planck-scale fluctuations in spacetime. We investigate the consequences of our findings for models of ultralight scalar dark matter.