R 4 counterterm and E 7(7) symmetry in maximal supergravity

Abstract

The coefficient of a potential R 4 counterterm in N = 8 supergravity has been shown previously to vanish in an explicit three-loop calculation. The R 4 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 continuous coset symmetry E 7(7)/SU(8) , exploring the limits as a single scalar becomes soft, as well as a double-soft scalar limit relation derived recently by Arkani-Hamed et al. We implement these relations for the matrix elements of the R 4 term that occurs in the low-energy expansion of closed-string tree-level amplitudes. We find that the matrix elements of R 4 that we investigated all obey the double-soft scalar limit relation, including certain non-maximally-helicity- violating six-point amplitudes. However, the single-soft limit does not vanish for this latter set of amplitudes, which suggests that the E 7(7) symmetry is broken by the R 4 term.