A double copy from twisted (co)homology at genus one

Abstract

We study the twisted (co)homology of a family of genus-one integrals -- the so called Riemann-Wirtinger integrals. These integrals are closely related to one-loop string amplitudes in chiral splitting where one leaves the loop-momentum, modulus and all but one puncture un-integrated. While not actual one-loop string integrals, they share many properties and are simple enough that the associated twisted (co)homologies have been completely characterized [Goto2022,arXiv:2206.03177]. Using intersection numbers -- an inner product on the vector space of allowed differential forms -- we derive the Gauss-Manin connection for two bases of the twisted cohomology providing an independent check of [Mano&Watanabe2012]. We also use the intersection index -- an inner product on the vector space of allowed contours -- to derive a double-copy formula for the closed-string analogues of Riemann-Wirtinger integrals (one-dimensional integrals over the torus). Similar to the celebrated KLT formula between open- and closed-string tree-level amplitudes, these intersection indices form a genus-one KLT-like kernel defining bilinears in meromorphic Riemann-Wirtinger integrals that are equal to their complex counterparts.

arXiv comment45+23 pages, 16 Figures. Updated to match version in JHEP. Text streamlined to focus on double copy result -- progress towards understanding Riemann-Wirtinger integrals in terms of eMPLs has been moved to appendix E

References in corpus (62)

• New Relations for Gauge-Theory Amplitudes
• Scattering of Massless Particles in Arbitrary Dimension
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• HPL, a Mathematica implementation of the harmonic polylogarithms
• Scattering Equations and KLT Orthogonality
• Integral Reduction with Kira 2.0 and Finite Field Methods
• HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
• Elliptic multiple zeta values and one-loop superstring amplitudes
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• Feynman Integrals and Intersection Theory
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Vector Space of Feynman Integrals and Multivariate Intersection Numbers
• Scattering Amplitudes from Intersection Theory
• One-loop amplitudes on the Riemann sphere
• Closed String Amplitudes as Single-Valued Open String Amplitudes
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Aspects of Scattering Amplitudes and Moduli Space Localization
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Decomposition of Feynman Integrals by Multivariate Intersection Numbers
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
• Monodromy Relations in Higher-Loop String Amplitudes
• Duals of Feynman Integrals, I: Differential Equations
• Higher-loop amplitude monodromy relations in string and gauge theory
• From Infinity to Four Dimensions: Higher Residue Pairings and Feynman Integrals
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Duals of Feynman Integrals, 2: Generalized Unitarity
• On a procedure to derive $\epsilon$-factorised differential equations beyond polylogarithms
• Baikov representations, intersection theory, and canonical Feynman integrals
• Constructing Canonical Feynman Integrals with Intersection Theory
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• Inverse of the String Theory KLT Kernel
• Numerical Scattering Amplitudes with pySecDec
• Cosmology meets cohomology
• Intersection numbers of twisted cycles and the correlation functions of the conformal field theory II
• FIRE 6.5: Feynman Integral Reduction with New Simplification Library
• Generalizations of the Double-Copy: the KLT Bootstrap
• Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
• One-loop open-string integrals from differential equations: all-order alpha'-expansions at n points
• Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes
• Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings
• Monodromy relations from twisted homology
• Disk Scattering of Open and Closed Strings (I)
• Superstring loop amplitudes from the field theory limit
• Towards the n-point one-loop superstring amplitude II: Worldsheet functions and their duality to kinematics
• One-loop monodromy relations on single cuts
• Functional relations for elliptic polylogarithms
• Loop amplitudes monodromy relations and color-kinematics duality
• Symbology for elliptic multiple polylogarithms and the symbol prime
• Properties of scattering forms and their relation to associahedra
• Lauricella hypergeometric functions, unipotent fundamental groups of the punctured Riemann sphere, and their motivic coactions
• Coaction and double-copy properties of configuration-space integrals at genus zero
• Prescriptive Unitarity with Elliptic Leading Singularities
• Intersection theory rules symbology
• On $\epsilon$-factorised bases and pure Feynman integrals
• Elliptic modular graph forms I: Identities and generating series
• An Infinite Family of Elliptic Ladder Integrals
• Two dialects for KZB equations: generating one-loop open-string integrals
• Periods and Superstring Amplitudes
• Feynman integral reduction using Gröbner bases
• Basis decompositions of genus-one string integrals

Cited by in corpus (6)

• Self-duality from twisted cohomology
• Twisted Riemann bilinear relations and Feynman integrals
• Differential equations for tree--level cosmological correlators with massive states
• Canonical differential equations and intersection matrices
• Twisted de Rham theory for string double copy in AdS
• A construction of single-valued elliptic polylogarithms