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arXiv · 2209.03922

A Symbol and Coaction for Higher-Loop Sunrise Integrals

Andreas Forum·Matt von Hippel
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Abstract

We construct a symbol and coaction for $l$-loop sunrise integrals, both for the equal-mass and generic-mass cases. These constitute the first concrete examples of symbols and coactions for integrals involving Calabi-Yau threefolds and higher. In order to achieve a symbol of finite length, we recast the differential equations satisfied by the master integrals of this topology in the form of a unipotent differential equation. We augment the basis of master integrals in a natural way by including ratios of maximal cuts $\tau_i$. We discuss the relationship of this construction to constructions of symbols and coactions for multiple polylogarithms and elliptic multiple polylogarithms, in particular its connection to notions of transcendental weight.

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Andreas Forum, Matt von Hippel. 2022-09-08. A Symbol and Coaction for Higher-Loop Sunrise Integrals. https://arxiv.org/abs/2209.03922

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