Effective Field Theory of Gravity to All Orders

TL;DR

The authors introduce GRSMEFT, a comprehensive effective field theory framework for gravity coupled to the Standard Model, constructed using Hilbert series and conformal representation theory to produce non-redundant operator bases to all orders. They demonstrate the method by deriving the pure gravity EFT up to dimension ten, the shift-symmetric scalar EFT coupled to gravity up to dimension eight, and the GRSMEFT basis up to dimension eight, with extensions to higher orders outlined. The Weyl tensor is established as the fundamental building block for gravitational operators, and redundancies from EOM and IBP are systematically addressed, enabling organized counting and construction of operators at successive mass dimensions. The results offer a formal, scalable path to connect low-energy gravity phenomenology with UV completions and to study inflationary, modified-gravity, and SM-gravity interactions in a unified EFT language.

Abstract

We construct the general effective field theory of gravity coupled to the Standard Model of particle physics, which we name GRSMEFT. Our method allows the systematic derivation of a non-redundant set of operators of arbitrary dimension with generic field content and gravity. We explicitly determine the pure gravity EFT up to dimension ten, the EFT of a shift-symmetric scalar coupled to gravity up to dimension eight, and the operator basis for the GRSMEFT up to dimension eight. Extensions to all orders are straightforward.