RG of GR from On-shell Amplitudes

TL;DR

This paper investigates the renormalization group flow of effective field theories with gravity using on-shell amplitudes, introducing a modified helicity to uncover new non-renormalization theorems and providing comprehensive one-loop results.

Contribution

It introduces a modified helicity concept for gravitons and applies on-shell amplitude methods to derive new non-renormalization theorems and detailed one-loop gravitational renormalization results.

Findings

Uncovered new non-renormalization theorems for theories with gravitons.

Provided complete one-loop gravitational renormalization results for gauge theories with matter.

Derived all-order results in the Planck mass for certain operators.

Abstract

We study the renormalization group of generic effective field theories that include gravity. We follow the on-shell amplitude approach, which provides a simple and efficient method to extract anomalous dimensions avoiding complications from gauge redundancies. As an invaluable tool we introduce a modified helicity $\tilde{h}$ under which gravitons carry one unit instead of two. With this modified helicity we easily explain old and uncover new non-renormalization theorems for theories including gravitons. We provide complete results for the one-loop gravitational renormalization of a generic minimally coupled gauge theory with scalars and fermions and all orders in $M_{Pl}$, as well as for the renormalization of dimension-six operators including at least one graviton, all up to four external particles.