  In this paper we study the coupled system of non-abelian gauge fields with
higher-derivative gravity. Charge renormalization is investigated in this
coupled system. It is found that the leading term in the gauge coupling beta
function comes due to interaction of gauge fields with gravitons. This is shown
to be a universal quantity in the sense that it doesn't depend on the gauge
coupling and the gauge group, but may depend on the other couplings of the
action (gravitational and matter). The coupled system is studied at one-loop.
It is found that the leading term of gauge beta function is zero at one-loop in
four dimensions. The effect of gauge fields on the running of gravitational
couplings is investigated. The coupled system of gauge field with
higher-derivative gravity is shown to satisfy unitarity when quantum
corrections are taken in to account. Moreover, it is found that Newton constant
goes to zero at short distances. In this renormalizable and unitary theory of
gauge field coupled with higher-derivative gravity, the leading term of the
gauge beta function, found to be universal for all gauge groups, is further
studied in more detail by isolating it in the context of abelian gauge theories
coupled with gravity in four dimensions. Using self-duality of abelian gauge
theories in four dimensions, this term of the gauge beta function is shown to
be zero to all loops. This is found to be independent of the gravity action,
regularization scheme and gauge fixing condition. An explicit one-loop
computation for arbitrary gravity action further demonstrates the vanishing of
this term in the gauge beta function in four dimensions, independent of the
regularization scheme and gauge fixing condition. Consequences of this are
discussed.
