Quantum Gravity in the Einstein-Yang-Mills Lagrangian
Absence of gravitational contributions to the running Yang-Mills coupling
We perform an involved diagrammatical calculation in the full (non-)abelian equation of state both in cut-off and dimensional regularization at one loop order.It is found that all gravitational quadratic divergencies cancel in cut-off regularization and are trivially absent in dimensional regularization so that there is no alteration to asymptotic freedom at high energies.The logarithmic divergencies give rise to an extended effective einstein-yang-mills lagrangian with a counterterm of dimension six.This counterterm can be removed by a nonlinear field redefinition of the gauge potential, producing a classical result of deser, tsao and van nieuwenhuizen obtained in the background field method with dimensional regularization.
