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

Abstract

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. The second class is given by so-called generalized elliptic integrands (GEIs) that are constructed using the same combinatorial patterns of the BRST pseudo-invariant superfields from part I. Both of them lead to compact and combinatorially rich expressions for the correlators in part III. The identities obeyed by the two classes of worldsheet functions exhibit striking parallels with those of the superfield kinematics. We will refer to this phenomenon as a duality between worldsheet functions and kinematics.

72 pages, v2: published version

References in corpus (6)

• The Momentum Kernel of Gauge and Gravity Theories
• The One-Loop Five-Graviton Amplitude and the Effective Action
• Current Algebra on the Torus
• Double-Copy Structure of One-Loop Open-String Amplitudes
• Towards the n-point one-loop superstring amplitude III: One-loop correlators and their double-copy structure
• Towards the n-point one-loop superstring amplitude I: Pure spinors and superfield kinematics

Cited by in corpus (20)

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• All-order differential equations for one-loop closed-string integrals and modular graph forms
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Towards the n-point one-loop superstring amplitude III: One-loop correlators and their double-copy structure
• Superstring loop amplitudes from the field theory limit
• Towards the n-point one-loop superstring amplitude I: Pure spinors and superfield kinematics
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• On integrands and loop momentum in string and field theory
• Loop amplitudes monodromy relations and color-kinematics duality
• All-order alpha'-expansion of one-loop open-string integrals
• Local BCJ numerators for ten-dimensional SYM at one loop
• A double copy from twisted (co)homology at genus one
• One-loop diagrams with quadratic propagators from the worldsheet
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Basis decompositions of genus-one string integrals
• Towards the underlying gauge theory of the pure spinor superstring
• Open-string integrals with multiple unintegrated punctures at genus one
• Advanced tools for basis decompositions of genus-one string integrals
• Pure spinor formulation of the superstring and its applications
• Tension between string amplitude prescriptions with presumed spacetime supersymmetry