Absence of gravitational contributions to the running Yang-Mills coupling

Understand

The question of a modification of the running gauge coupling of (non-) abelian gauge theories by an incorporation of the quantum gravity contribution has recently attracted considerable interest.

• In this letter we perform an involved diagrammatical calculation in the full Einstein-Yang-Mills system 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.