Correction to the Running of Gauge Couplings out of Extra Dimensional Gravity

We study the gravitational correction to the gauge couplings in the extra dimension model where the gravity propagates in the (4+n)-dimensional bulk. We show by explicit calculation in the background field method that the one-loop correction coming from graviton Kaluza-Klein states is nontrivial and tends to make the theory anti-asymptotically free. For the theory characterized with asymptotic freedom, the correction will induce a nontrivial UV-stable fixed point. This may lead to an interesting possibility that the non-abelian gauge coupling constants $g_2$ and $g_3$ in the SM and that of the gravity $g_{\kappa}$ unify at the fixed point in the limit of high energy scale.