Two-loop superstrings and S-duality

The two-loop contribution to the type IIB low energy effective action term D(4)R4(4) predicted by SL(2, Z) duality, is compared with that of the two-loop 4-point function derived recently in super-string 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 (DR4)-R-4 match exactly, thus providing an indirect check of SL(2, Z) duality. The two-loop heterotic low energy term (DF4)-F-2 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. (c) 2005 Elsevier B.V. All rights reserved.