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

Abstract

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. Interestingly, the expression for the eight-point correlator following from our method seems to capture correctly all the dependence on the worldsheet punctures but leaves undetermined the coefficient of the holomorphic Eisenstein series ${\mathrm{G}}_4$. By virtue of chiral splitting, closed-string correlators follow from the double copy of the open-string results.

77 pages, v2: published version

References in corpus (10)

• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• Gluons and gravitons at one loop from ambitwistor strings
• The One-Loop Five-Graviton Amplitude and the Effective Action
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• 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
• The One-loop Open Superstring Massless Five-point Amplitude with the Non-Minimal Pure Spinor Formalism
• Towards the n-point one-loop superstring amplitude II: Worldsheet functions and their duality to kinematics
• Towards the n-point one-loop superstring amplitude I: Pure spinors and superfield kinematics

Cited by in corpus (23)

• Weyl doubling
• Tree-level amplitudes from the pure spinor superstring
• All-order differential equations for one-loop closed-string integrals and modular graph forms
• One-loop Correlators and BCJ Numerators from Forward Limits
• Towards the n-point one-loop superstring amplitude III: One-loop correlators and their double-copy structure
• Generating series of all modular graph forms from iterated Eisenstein integrals
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Superstring loop amplitudes from the field theory limit
• Towards the n-point one-loop superstring amplitude II: Worldsheet functions and their duality to kinematics
• 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
• All-order alpha'-expansion of one-loop open-string integrals
• Local BCJ numerators for ten-dimensional SYM at one loop
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• Two-loop superstring five-point amplitudes III, construction via the RNS formulation: even spin structures
• 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
• 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