R4 Counterterm and E7(7) Symmetry in Maximal Supergravity

The coefficient of a potential R4 counterterm in N = 8 supergravity has been shown previously to vanish in an explicit three-loop calculation. The R4 term respects N = 8 supersymmetry; hence this result poses the question of whether another symmetry could be responsible for the cancellation of the three-loop divergence. In this article we investigate possible restrictions from the coset symmetry E7(7)/SU(8), using a double-soft scalar limit relation derived recently by Arkani-Hamed et al. In order to implement the relation, we make use of the fact that the R4 term occurs in the low-energy expansion of closed-string tree-level amplitudes. We find that the matrix elements of R4 that we investigated all obey the double-soft scalar limit relation, suggesting that E7(7) is also respected by the R4 term.