  This paper investigates the coupling of massive fermions to gravity within
the context of a non-Abelian gauge theory, utilizing the effective field theory
framework for quantum gravity. Specifically, we calculate the two-loop beta
function of the gauge coupling constant in a non-Abelian gauge theory,
employing the one-graviton exchange approximation. Our findings reveal that
gravitational corrections may lead to a non-trivial UV fixed point in the beta
function of the gauge coupling constant, contingent upon the specific gauge
group and the quantity of fermions involved.
