Abstract
In string theories, one-loop scattering amplitudes are characterized by integrals over genus-one surfaces using the Kronecker-Eisenstein series. A recent methodology proposed a genus-one basis formed from products of these series of chain topologies. A prior work further deconstructed cyclic products of the Kronecker-Eisenstein series on this basis. Building on it, our study further employs advanced and comprehensive combinatorial techniques to decompose more general genus-one integrands including a product of an arbitrary number of cyclic products of Kronecker-Eisenstein series, supplemented by Mathematica codes. Our insights enhance the understanding of multiparticle amplitudes across various string theories and illuminate loop-level parallels with string tree-level amplitudes.
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Acknowledgments
We would like to thank Carlos Rodriguez and Oliver Schlotterer for constructive feedback on our manuscript and collaboration on related topics. Our appreciation also extends to Freddy Cachazo and Song He for useful discussions. The research of Y.Z. was 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. The research of Y.Z. was also supported by the Knut and Alice Wallenberg Foundation under the grant KAW 2018.0116: From Scattering Amplitudes to Gravitational Waves.
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Zhang, Y. Advanced tools for basis decompositions of genus-one string integrals. J. High Energ. Phys. 2024, 255 (2024). https://doi.org/10.1007/JHEP05(2024)255
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DOI: https://doi.org/10.1007/JHEP05(2024)255