On the finiteness of N=8 quantum supergravity

TL;DR

The paper investigates whether N=8 quantum supergravity is perturbatively finite by leveraging duality symmetries from string theory and the AdS/CFT correspondence. It analyzes the graviton S-matrix in IIB string theory, organizes perturbative terms with modular functions, and shows genus truncation and monopole/dyon dual descriptions constrain higher-loop contributions. Through AdS/CFT and planar limits, it argues that the maximum allowed genus for a term Box^k R^4 is finite, and that cancellations persist through multiple loops, suggesting finiteness in d=4--6 under dualities. While not rigorously proven, the results provide strong evidence that duality structures could render N=8 supergravity perturbatively finite and tightly constrain quantum gravity in highly supersymmetric settings.

Abstract

We describe the constraints imposed on quantum maximal supergravity theories in perturbation theory by the two duality frameworks: S-duality in superstring theory and the AdS/CFT holographic correspondence between IIB superstring theory and N=4 super Yang-Mills theory.