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Higher Loop Spin Field Correlators in Various Dimensions

We compute higher-point superstring correlators involving spin fields in various even space-time dimensions 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 correlation 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 <psi ... psi SS> with any number of fermions psi and two spin fields S in D space-time dimensions is given for arbitrary genus. Moreover, in D=6 and for arbitrary genus, we find a general formula for the correlators <S dot S ... S dot S>. 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.