New higher-derivative R4 theorems for graviton scattering.
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, partial differential(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< or =8, perturbative contributions to partial differential(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.
Berkovits
Nathan
N
Instituto de Física Teórica, State University of São Paulo, Rua Pamplona 145, 01405-900, São Paulo, SP, Brasil. nberkovi@ift.unesp.br