R^4 counterterm and E7(7) symmetry in maximal supergravity

Understand

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 coset symmetry E7(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.