New Higher-DerivativeR4Theorems 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 ${R}^{4}$ conjectures of Green, Russo, and Vanhove. The first theorem states that when $0<n<12$, ${\ensuremath{\partial}}^{n}{R}^{4}$ terms in the Type II effective action do not receive perturbative contributions above $n/2$ loops. The second theorem states that when $n\ensuremath{\le}8$, perturbative contributions to ${\ensuremath{\partial}}^{n}{R}^{4}$ 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.