From maximal to minimal supersymmetry in string loop amplitudes

TL;DR

This paper develops a method to compute one-loop string amplitudes with minimal supersymmetry, organizing contributions from all spin structures, and explores implications for string effective actions.

Contribution

It introduces a novel approach to combine spin structure contributions for arbitrary legs in minimal supersymmetry string amplitudes and reorganizes integrals into a compact form.

Findings

Successfully computed one-loop amplitudes for various supersymmetries and dimensions.

Reorganized amplitudes into a compact form using basis of kinematic blocks.

Discussed implications for the structure of the one-loop string effective action.

Abstract

We calculate one-loop string amplitudes of open and closed strings with N=1,2,4 supersymmetry in four and six dimensions, by compactification on Calabi-Yau and K3 orbifolds. In particular, we develop a method to combine contributions from all spin structures for an arbitrary number of legs at minimal supersymmetry. Each amplitude is cast into a compact form by reorganizing the kinematic building blocks and casting the worldsheet integrals in a basis. Infrared regularization plays an important role to exhibit the expected factorization limits. We comment on implications for the one-loop string effective action.