Constraints on radion vev from the beta functions for top yukawa coupling and higgs self coupling in the Randall-Sundrum model

In this paper we determine how the beta function for the top Yukawa coupling to one loop is modified by a light stabilized radion in the Randall-Sundrum model. We then use this beta function together with \beta (\lambda) to deteremine lower bounds on the radion vev <\phi> for different values of \lambda(m_z) and m_{\phi} by demanding that both g_t(\mu) and \lambda(\mu) should remain perturbative from m_z up ot the cut off \Lambda. We find that the lower bounds on <\phi> that follow from the condition \lambda(\Lambda)<\sqrt{4\pi} nearly agree with those that follow from g_t(\Lambda)<\sqrt{4\pi}. We have also determined the critical value of <\phi> for different values of \lambda(m_z) and m_{\phi} from the line of fixed points which is given by \beta(g_t)=0.