Abstract
We obtain the exact non-perturbative thresholds of R 4 terms in type 1113 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-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(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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