Contents

We compute higher-point superstring correlators involving spin fields in various even space-time dimen-sions D at tree-level and to arbitrary loop order. This generalizes previous work in D = 4 space-time dimensions. The main focus are D = 6, 8 and D = 10 superstring compactifications for which cor-relation functions with four and more spin fields are computed. More precisely, we present every non-vanishing six-point function. A number of results can even be derived for arbitrary D. A closed formula for the correlators 〈ψ... ψSS 〉 with any number of fermions ψ and two spin fields S in D space-time dimensions is given for arbitrary genus. Moreover, inD = 6 and for arbitrary genus, we find a general formula for the correlators 〈SS ̇... SṠ〉. The latter serve as basic building blocks to construct higher-point fermionic correlation functions. In D = 8 we can profit from the SO(8)-triality to derive further tree-level correlators with a large numbers of spin fields. MPP–2010–2 ar X i