Towards the n-point one-loop superstring amplitude III: One-loop correlators and their double-copy structure

Understand

In this final part of a series of three papers, we will assemble supersymmetric expressions for one-loop correlators in pure-spinor superspace that are BRST invariant, local, and single valued.

• A key driving force in this construction is the generalization of a so far unnoticed property at tree level; the correlators have the symmetry structure akin to Lie polynomials.
• One-loop correlators up to seven points are presented in a variety of representations manifesting different subsets of their defining properties.
• These expressions are related via identities obeyed by the kinematic superfields and worldsheet functions spelled out in the first two parts of this series and reflecting a duality between the two kinds of ingredients.