Genus one super-Green function revisited and superstring amplitudes with non-maximal supersymmetry

TL;DR

This paper revisits genus one super-Green functions with twisted boundary conditions, deriving new series expressions, and applies these to compute one-loop superstring amplitudes in models with non-maximal supersymmetry, exemplified by open string orbifolds.

Contribution

It provides a new series representation for genus one super-Green functions with general boundary conditions and applies this to calculate superstring amplitudes with reduced supersymmetry.

Findings

Derived hypergeometric series expressions for super-Green functions.

Computed one-loop superstring amplitudes in non-maximal supersymmetric models.

Analyzed massless vector emissions in open string orbifold scenarios.

Abstract

We reexamine genus one super-Green functions with general boundary conditions twisted by $(\alpha, \beta)$ for $(\sigma, \tau)$ directions in the eigenmode expansion and derive expressions as infinite series of hypergeometric functions. Using these, we compute one-loop superstring amplitudes with non-maximal supersymmetry, taking an example of massless vector emissions of open string type I ${\cal Z}_2$ orbifold.