Running couplings and operator mixing in the gravitational corrections to coupling constants

Understand

The use of a running coupling constant in renormalizable theories is well known, but the implementation of this idea for effective field theories with a dimensional coupling constant is in general less useful.

• Nevertheless there are multiple attempts to define running couplings including the effects of gravity, with varying conclusions.
• We sort through many of the issues involved, most particularly the idea of operator mixing and also the kinematics of crossing, using calculations in Yukawa and lambda phi^4 theory as illustrative examples.
• We remain in the perturbative regime.