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. We introduce a 'modified helicity’, under which gravitons carry one unit instead of two, and use it to explain old and uncover new non-renormalization theorems for theories including gravitons. In this talk I will provide results for the one-loop renormalization of a generic minimally coupled gauge theory with scalars and fermions.
Our results have interesting applications in theoretical studies of quantum gravity. In this talk I will in particular comment on the implications of the sign of gravitational anomalous dimensions on positivity bounds for Wilson coefficients of dimension eight operators.