标题： 从Zeta生成元出发的单值共作用研究 显示英文标题

标题： Towards Motivic Coactions at Genus One from Zeta Generators

摘要： 多重zeta值和多重多对数的动机共作用在各种量子场论和弦理论中的散射幅度的结构洞察和计算方法中编码了重要的信息。 在本工作中，我们提出了来自 genus 一配置空间积分的全纯Eisenstein级数的迭代积分的共作用公式。 我们的提议是基于最近通过zeta生成元重新表述的零genus下多重多对数的动机共作用和单值映射之间的形式相似性。 然后，通过类比于利用zeta生成元在genus 一构造单值迭代Eisenstein积分的方法，提出了本工作中的genus一共作用。 我们证明了我们的提议表现出共作用预期的性质，并推导了从正则化极限得到的多重模值的$f$-字母分解。 显示英文摘要

摘要： 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.