  Exact non-perturbative results have been conjectured for R^4 couplings in
type II maximally supersymmetric string theory. Strong evidence has already
been obtained, but contributions of cusp forms, invisible in perturbation
theory, have remained an open possibility. In this note, we use the D=8 N=2
superfield formalism of Berkovits to prove that supersymmetry requires the
exact R^4 threshold to be an eigenmode of the Laplacian on the scalar manifold
with a definite eigenvalue. Supersymmetry and U-duality invariance then
identify the exact result with the order-3/2 Eisenstein series, and rule out
cusp form contributions.
