RG of GR from on-shell amplitudes

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 (h) over tilde 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-P1, as well as for the renormalization of dimension-six operators including at least one graviton, all up to four external particles.

Automated summary

In this study, we investigate the renormalization group of generic effective field theories with gravity, using the on-shell amplitude approach. We introduce a modified helicity to simplify the extraction of anomalous dimensions and apply it to explain old and discover new non-renormalization theorems for theories involving gravitons. Furthermore, we provide complete results for the one-loop gravitational renormalization of a generic minimally coupled gauge theory and the renormalization of dimension-six operators with at least one graviton, up to four external particles.