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Poincaré series for modular graph forms at depth two. Part I. Seeds and Laplace systems

Dorigoni, Daniele; Kleinschmidt, Axel; Schlotterer, Oliver

Poincaré series for modular graph forms at depth two. Part I. Seeds and Laplace systems Thumbnail


Authors

Axel Kleinschmidt

Oliver Schlotterer



Abstract

We derive new Poincaré-series representations for infinite families of non-holomorphic modular invariant functions that include modular graph forms as they appear in the low-energy expansion of closed-string scattering amplitudes at genus one. The Poincaré series are constructed from iterated integrals over single holomorphic Eisenstein series and their complex conjugates, decorated by suitable combinations of zeta values. We evaluate the Poincaré sums over these iterated Eisenstein integrals of depth one and deduce new representations for all modular graph forms built from iterated Eisenstein integrals at depth two. In a companion paper, some of the Poincaré sums over depth-one integrals going beyond modular graph forms will be described in terms of iterated integrals over holomorphic cusp forms and their L-values.

Citation

Dorigoni, D., Kleinschmidt, A., & Schlotterer, O. (2022). Poincaré series for modular graph forms at depth two. Part I. Seeds and Laplace systems. Journal of High Energy Physics, 2022, Article 133. https://doi.org/10.1007/jhep01%282022%29133

Journal Article Type Article
Acceptance Date Dec 24, 2021
Online Publication Date Jan 25, 2022
Publication Date 2022
Deposit Date Oct 12, 2021
Publicly Available Date Feb 7, 2022
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Electronic ISSN 1029-8479
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2022
Article Number 133
DOI https://doi.org/10.1007/jhep01%282022%29133

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.





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