Divergences and Boundary Modes in N=8 Supergravity

Understand

We reconsider the one loop divergence of ${\cal N}=8$ supergravity in four dimensions.

• We compute the finite effective potential of ${\cal N}=8$ anti-deSitter supergravity and interpret it as logarithmic running of the cosmological constant.
• We find that quantum inequivalence between fields that are classically dual is due to boundary modes in AdS$_4$.
• Some subtleties are traced to the difference between the Euler characteristic of global and thermal AdS$_4$.