One loop amplitude for Heterotic string on $T^2$

TL;DR

This paper recalculates one-loop amplitudes for heterotic string theory compactified on a torus, providing detailed elliptic genus and amplitude results for various gauge groups, enhancing understanding of string compactifications.

Contribution

It presents a comprehensive calculation of one-loop amplitudes and elliptic genus for heterotic strings on $T^2$, including cases with Wilson lines and multiple gauge groups.

Findings

Complete elliptic genus for heterotic strings on $T^2$

Harmonic part of CP-even amplitude for various gauge groups

Results applicable to string compactification studies

Abstract

We revisit the results of one loop string amplitude calculations for the Heterotic string theory compactified on a torus with or without Wilson lines. We give the complete elliptic genus and the harmonic part of the CP-even amplitude for the gauge groups $SO(32)$, $E_8 \times E_8$, $SO(16)^2$ and $SO(8)^4$.