One Loop Superstring Effective Actions and N = 8 Supergravity

In a previous article we have shown the existence of a new independent R4 term, at one loop, in the type IIA and heterotic effective actions, after reduction to four dimensions, besides the usual square of the Bel-Robinson tensor. It had been shown that such a term could not be directly supersymmetrized, but we showed that was possible after coupling to a scalar chiral multiplet. In this article we study the extended (N = 8) supersymmetrization of this term, where no other coupling can be taken. We show that such supersymmetrization cannot be achieved at the linearized level. This is in conflict with the theory one gets after toroidal compactification of type II superstrings being N = 8 supersymmetric. We interpret this result in face of the recent claim that perturbative supergravity cannot be decoupled from string theory in d ≥ 4, and N = 8, d = 4 supergravity is in the swampland.