R⁴ counterterm and E 7(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 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 R⁴ term that occurs in the low-energy expansion of closed-string treelevel amplitudes. We find that the matrix elements of R⁴ that we investigated all obey the double-soft scalar limit relation, including certain non-maximally-helicity-violating sixpoint 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 R⁴ term.