On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons

Details On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons

1997-07-01

arxiv.org/abs/hep-th/9707018v6

Nucl.Phys.B508:509-534,1997

Physics

High Energy Physics

High Energy Physics - Theory

24 pages; v6: Eqs 5.27, 5.28 fixed, refs updated, see note added

Scientific paper

10.1016/S0550-3213(97)00645-7

We obtain the exact non-perturbative thresholds of $R^4$ terms in IIB string theory compactified to eight and seven dimensions. These thresholds are given by the perturbative tree-level and one-loop results together with the contribution of the D-instantons and of the (p,q)-string instantons. The invariance under U-duality is made manifest by rewriting the sum as a non-holomorphic modular function of the corresponding discrete U-duality group. In the eight-dimensional case, the threshold is the sum of a order-1 Eisenstein series for SL(2,Z) and a order-3/2 Eisenstein series for SL(3,Z). The seven-dimensional result is given by the order-3/2 Eisenstein series for SL(5,Z). We also conjecture formulae for the non-perturbative thresholds in lower dimensional compactifications and discuss the relation with M-theory.

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