Divergences and boundary modes in N=8 supergravity

We reconsider the one loop divergence of N=8 supergravity in four dimensions. We compute the finite effective potential of N=8 anti-deSitter supergravity and interpret it as logarithmic running of the cosmological constant. We show that quantum inequivalence between fields that are classically dual is due to boundary modes in AdS₄. The boundary modes are important in global AdS₄ but not in thermal AdS₄ since these geometries have different Euler characteristic.