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

TL;DR

This paper examines the role of E7(7) symmetry in N=8 supergravity's R^4 counterterm, finding that the symmetry appears broken by the R^4 term despite certain soft scalar limits being satisfied.

Contribution

The study investigates E7(7) symmetry constraints on the R^4 counterterm in supergravity, revealing potential symmetry breaking.

Findings

R^4 matrix elements obey double-soft scalar limit relations

Single-soft scalar limit does not vanish for certain amplitudes

E7(7) symmetry may be broken by the R^4 term

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.