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.
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Acknowledgments
We would like to thank Rishabh Bhardwaj, Freddy Cachazo, Alex Edison, Max Guillen, Song He, Andrzej Pokraka, Lecheng Ren and in particular Filippo Balli for combinations of valuable discussions and collaboration on related topics. C.R. and O.S. are supported by the European Research Council under ERC-STG-804286 UNISCAMP. The research of Y.Z. is supported by the Knut and Alice Wallenberg Foundation under the grant KAW 2018.0116: From Scattering Amplitudes to Gravitational Waves. The research of Y.Z. was also supported in part by a grant from the Gluskin Sheff/Onex Freeman Dyson Chair in Theoretical Physics and by Perimeter Institute. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities.
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Rodriguez, C., Schlotterer, O. & Zhang, Y. Basis decompositions of genus-one string integrals. J. High Energ. Phys. 2024, 256 (2024). https://doi.org/10.1007/JHEP05(2024)256
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DOI: https://doi.org/10.1007/JHEP05(2024)256