Towards Motivic Coactions at Genus One from Zeta Generators
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| Format: | Preprint |
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2025
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| _version_ | 1866909012869513216 |
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| author | Kleinschmidt, Axel Porkert, Franziska Schlotterer, Oliver |
| author_facet | Kleinschmidt, Axel Porkert, Franziska Schlotterer, Oliver |
| contents | The motivic coaction of multiple zeta values and multiple polylogarithms encodes both structural insights on and computational methods for scattering amplitudes in a variety of quantum field theories and in string theory. In this work, we propose coaction formulae for iterated integrals over holomorphic Eisenstein series that arise from configuration-space integrals at genus one. Our proposal is motivated by formal similarities between the motivic coaction and the single-valued map of multiple polylogarithms at genus zero that are exposed in their recent reformulations via zeta generators. The genus-one coaction of this work is then proposed by analogies with the construction of single-valued iterated Eisenstein integrals via zeta generators at genus one. We show that our proposal exhibits the expected properties of a coaction and deduce $f$-alphabet decompositions of the multiple modular values obtained from regularized limits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards Motivic Coactions at Genus One from Zeta Generators Kleinschmidt, Axel Porkert, Franziska Schlotterer, Oliver High Energy Physics - Theory Algebraic Geometry Number Theory The motivic coaction of multiple zeta values and multiple polylogarithms encodes both structural insights on and computational methods for scattering amplitudes in a variety of quantum field theories and in string theory. In this work, we propose coaction formulae for iterated integrals over holomorphic Eisenstein series that arise from configuration-space integrals at genus one. Our proposal is motivated by formal similarities between the motivic coaction and the single-valued map of multiple polylogarithms at genus zero that are exposed in their recent reformulations via zeta generators. The genus-one coaction of this work is then proposed by analogies with the construction of single-valued iterated Eisenstein integrals via zeta generators at genus one. We show that our proposal exhibits the expected properties of a coaction and deduce $f$-alphabet decompositions of the multiple modular values obtained from regularized limits. |
| title | Towards Motivic Coactions at Genus One from Zeta Generators |
| topic | High Energy Physics - Theory Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2508.02800 |