R^4 counterterm and E7(7) symmetry in maximal supergravity
J. Broedel, L. J. Dixon
TL;DR
The authors test whether the E7(7)/SU(8) coset symmetry can restrict the R^4 counterterm in N=8 supergravity by examining α'-corrected closed-string tree-level amplitudes. Using KLT relations and N=4/N=1 SUSY Ward identities, they construct α'^3 corrections to six-point NMHV amplitudes and analyze their soft limits, focusing on single- and double-soft scalar emissions. They find that the double-soft limit obeys the Arkani-Hamed–Cachazo–Kaplan relation, suggesting a compatibility with E7(7) at this order, but the single-soft limit does not vanish for certain NMHV amplitudes, indicating that E7(7) is broken by the R^4 term. Consequently, the observed three-loop finiteness cannot be solely attributed to E7(7) symmetry, though the double-soft behavior hints at subtle symmetry structures that warrant further investigation across higher-point amplitudes and scalar couplings.
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 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. 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 E7(7) symmetry is broken by the R^4 term.