Two-loop superstrings and S-duality

The two-loop contribution to the type IIB low energy effective action term D4R4, predicted by SL(2,Z) duality, is compared with that of the two-loop 4-point function derived recently in superstring perturbation theory through the method of projection onto super period matrices. For this, the precise overall normalization of the 4-point function is determined through factorization. The resulting contributions to D4R4 match exactly, thus providing an indirect check of SL(2,Z) duality. The two-loop heterotic low energy term D2F4 is evaluated in string perturbation theory; its form is closely related to the D4R4 term in type II, although its significance to duality is an open issue