Heterotic type I duality and D-brane instantons

We study heterotic/type I duality in d = 8,9 uncompactified dimensions. We consider the special ("BPS-saturated") F-4 and R-4 terms in the effective one-loop heterotic action, which are expected to be non-perturbatively exact. Under the standard duality map these translate to tree-level, perturbative and non-perturbative contributions on the type I side. We check agreement with the one-loop open string calculation, and discuss the higher-order perturbative contributions, which arise because of the mild non-holomorphicities of the heterotic elliptic genus. We put the heterotic world-sheet instanton corrections in a form that can be motivated as arising from a D-brane instanton calculation on the type I side. (C) 1998 Elsevier Science B.V.