ON R-4 THRESHOLD CORRECTIONS IN TYPE IIB STRING THEORY AND (P,Q)-STRING INSTANTONS

We obtain the exact non-perturbative thresholds of R-4 terms in type I IB string theory compactified to eight and seven dimensions. These thr esholds are given by the perturbative tree-level and one-loop results together with the contribution of the D-instantons and of the (p,q)-st ring instantons. The invariance under U-duality is made manifest by re writing the sum as a nonholomorphic-invariant modular function of the corresponding discrete U-duality group, In the eight-dimensional case, the threshold is the sum of an order-1 Eisenstein series for SL(2,Z) and an order-3/2 Eisenstein series for SL(3,Z). The seven-dimensional result is given by the order-3/2 Eisenstein series for SL(S,Z). We als o conjecture formulae for the non-perturbative thresholds in lower-dim ensional compactifications and discuss the relation with M-theory. (C) 1997 Elsevier Science B.V.