Higher Loop Spin Field Correlators in Various Dimensions

TL;DR

This paper computes higher-point superstring correlators involving spin fields across various even dimensions, providing explicit formulas and extending previous work mainly focused on four-dimensional space-time.

Contribution

It generalizes superstring correlator calculations to higher dimensions and arbitrary genus, offering explicit formulas for six-point functions and beyond, including new results in D=6,8, and 10.

Findings

Explicit six-point correlators in D=6,8,10

Closed formulas for fermionic correlators with multiple spin fields

Utilization of SO(8)-triality for deriving correlators in D=8

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 <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.