# Towards the n-point one-loop superstring amplitude I: Pure spinors and superfield kinematics

## TL;DR

This paper introduces a method to compute higher-point one-loop superstring amplitudes using pure spinor superspace and superfield kinematics, laying the groundwork for a series of detailed studies.

## Contribution

It develops a novel approach combining pure-spinor superspace cohomology with zero-mode integration to analyze multiparticle superfields in superstring theory.

## Key findings

- Identification of local, covariant superfields with BRST variations
- Connection between superfield properties and generalized elliptic integrands
- Review and reinterpretation of BRST pseudo-invariants

## Abstract

This is the first installment of a series of three papers in which we describe a method to determine higher-point correlation functions in one-loop open-superstring amplitudes from first principles. In this first part, we exploit the synergy between the cohomological features of pure-spinor superspace and the pure-spinor zero-mode integration rules of the one-loop amplitude prescription. This leads to the study of a rich variety of multiparticle superfields which are local, have covariant BRST variations, and are compatible with the particularities of the pure-spinor amplitude prescription. Several objects related to these superfields, such as their non-local counterparts and the so-called BRST pseudo-invariants, are thoroughly reviewed and put into new light. Their properties will turn out to be mysteriously connected to products of one-loop worldsheet functions in packages dubbed "generalized elliptic integrands", whose prominence will be seen in the later parts of this series of papers.

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Source: https://tomesphere.com/paper/1812.10969