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.

45+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 (19)

• New Relations for Gauge-Theory Amplitudes
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• On a procedure to derive $\epsilon$-factorised differential equations beyond polylogarithms
• Duals of Feynman Integrals, 2: Generalized Unitarity
• Cosmology meets cohomology
• Numerical Scattering Amplitudes with pySecDec
• FIRE 6.5: Feynman Integral Reduction with New Simplification Library
• Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
• Monodromy relations from twisted homology
• One-loop monodromy relations on single cuts
• Symbology for elliptic multiple polylogarithms and the symbol prime
• Intersection theory rules symbology
• On $\epsilon$-factorised bases and pure Feynman integrals
• An Infinite Family of Elliptic Ladder Integrals
• 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