Higher loop spin field correlators in various dimensions

Abstract

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 〈 ψ … ψ S S 〉 with any number of fermions ψ 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 S ˙ … S 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.