On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons
Abstract
We obtain the exact non-perturbative thresholds of 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.
Cite
@article{arxiv.hep-th/9707018,
title = {On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons},
author = {Elias Kiritsis and Boris Pioline},
journal= {arXiv preprint arXiv:hep-th/9707018},
year = {2010}
}
Comments
24 pages; v6: Eqs 5.27, 5.28 fixed, refs updated, see note added