Divergences and Boundary Modes in N=8 Supergravity

TL;DR

This work analyzes the one-loop structure of ${\cal N}=8$ AdS$_4$ supergravity using heat-kernel techniques, revealing a finite logarithmic running of the cosmological constant rather than power-law divergences. The authors show that quantum inequivalence between dual fields, such as a massless 2-form and its scalar dual, is physical and arises from boundary modes in AdS$_4$, with the outcome depending on the Euler characteristic of the spacetime boundary. They connect these bulk phenomena to a preferred duality frame from 11D supergravity on $S^7$ where boundary-mode contributions cancel, illustrating a topological origin for divergences via the Gauss-Bonnet theorem. The findings suggest a nuanced picture where topology, boundary conditions, and duality frames jointly determine quantum corrections to the cosmological constant, with potential implications for naturalness and the role of boundary data in holography.

Abstract

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$_4$.