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.

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.