RG of GR from On-shell Amplitudes

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.

arXiv comment52 pages, 9 figures, 5 appendices

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• Positivity bounds in the Standard Model effective field theory beyond tree level
• Renormalization of the Standard Model Effective Field Theory from Geometry
• Causality Constraints on Black Holes beyond GR
• Amplitude bases in generic EFTs
• Building blocks of the flavourful SMEFT RG
• Gearing up for the next generation of LFV experiments, via on-shell methods
• Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
• Renormalization of effective field theories via on-shell methods: the case of axion-like particles
• Dimension-8 SMEFT contact-terms for vector-pair production via on-shell Higgsing
• Renormalising the Field-Space Geometry
• A Green's basis for the bosonic SMEFT to dimension 8