Towards the n-point one-loop superstring amplitude II: Worldsheet functions and their duality to kinematics

Understand

This is the second 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 second part, we study worldsheet functions defined on a genus-one surface built from the coefficient functions of the Kronecker--Einsenstein series.
• We construct two classes of worldsheet functions whose properties lead to several simplifying features within our description of one-loop correlators with the pure-spinor formalism.
• The first class is described by functions with prescribed monodromies, whose characteristic shuffle-symmetry property leads to a Lie-polynomial structure when multiplied by the local superfields from part I of this series.