Basis decompositions of genus-one string integrals

Abstract

One-loop scattering amplitudes in string theories involve configuration-space integrals over genus-one surfaces with coefficients of Kronecker-Eisenstein series in the integrand. A conjectural genus-one basis of integrands under Fay identities and integration by parts was recently constructed out of chains of Kronecker-Eisenstein series. In this work, we decompose a variety of more general genus-one integrands into the conjectural chain basis. The explicit form of the expansion coefficients is worked out for infinite families of cases where the Kronecker-Eisenstein series form cycles. Our results can be used to simplify multiparticle amplitudes in supersymmetric, heterotic and bosonic string theories and to investigate loop-level echoes of the field-theory double-copy structures of string tree-level amplitudes. The multitude of basis reductions in this work strongly validate the recently proposed chain basis and stimulate mathematical follow-up studies of more general configuration-space integrals with additional marked points or at higher genus.

56+8 pages, 9 figures. The companion paper 2403.18078 provides a Mathematica implementation. v2: minimal cosmetic changes, matches the published version in JHEP

References in corpus (11)

• New Relations for Gauge-Theory Amplitudes
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills
• String predictions for near future colliders from one-loop scattering amplitudes around D-brane worlds
• Duals of Feynman Integrals, 2: Generalized Unitarity
• Current Algebra on the Torus
• All-order differential equations for one-loop closed-string integrals and modular graph forms
• Generating series of all modular graph forms from iterated Eisenstein integrals
• Monodromy relations from twisted homology
• Advanced tools for basis decompositions of genus-one string integrals

Cited by in corpus (2)

• A double copy from twisted (co)homology at genus one
• Advanced tools for basis decompositions of genus-one string integrals