RG of GR from on-shell amplitudes
Pietro Baratella, Dominik Haslehner, Maximilian Ruhdorfer, Javi Serra, Andreas Weiler
Abstract
A bstract 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 $$ \tilde{h} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>h</mml:mi> <mml:mo>˜</mml:mo> </mml:mover> </mml:math> 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.