Effective field theory of gravity to all orders

Maximilian Ruhdorfer,Javi Serra,Andreas Weiler

doi:10.1007/jhep05(2020)083

Maximilian Ruhdorfer, Javi Serra + Show 1 more

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https://doi.org/10.1007/jhep05(2020)083

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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.

Highlights

Effective field theory (EFT) lies at the core of our modern understanding of the fundamental interactions in nature
A subtle problem is that of finding a non-redundant operator basis for the EFT, something that is key in order to properly identify the independent directions in the space of all possible UV completions of the EFT, i.e. the most general set of physically different deformations of the leading dynamics
Our approach relies on Hilbert series and conformal representation theory, and makes use of the Weyl tensor as basic building block of gravitational operators

Summary

Introduction

Effective field theory (EFT) lies at the core of our modern understanding of the fundamental interactions in nature. A subtle problem is that of finding a non-redundant operator basis for the EFT, something that is key in order to properly identify the independent directions in the space of all possible UV completions of the EFT, i.e. the most general set of physically different deformations of the leading dynamics. This issue is non-trivial because, in general, seemingly independent operators can be related by the equations of motion, partial integration and algebraic identities. This problem has been recently solved for the EFT of the Standard Model of particle physics (known as SMEFT) [1, 2], the method relying on Hilbert series and, to a lesser extent, conformal representation theory

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