New higher-derivative R-4 theorems for graviton scattering

Abstract

The nonminimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative R4 conjectures of Green, Russo, and Vanhove. The first theorem states that when 0<n<12, nR4 terms in the Type II effective action do not receive perturbative contributions above n/2 loops. The second theorem states that when n≤8, perturbative contributions to nR4 terms in the IIA and IIB effective actions coincide. As shown by Green, Russo, and Vanhove, these results suggest that d=4 N=8 supergravity is ultraviolet finite up to eight loops. © 2007 The American Physical Society.