A symbol and coaction for higher-loop sunrise integrals

Forum, Andreas; von Hippel, Matt

doi:10.21468/SciPostPhysCore.6.3.050

SciPost Physics Core

A symbol and coaction for higher-loop sunrise integrals

Andreas Forum, Matt von Hippel

SciPost Phys. Core 6, 050 (2023) · published 12 July 2023

doi: 10.21468/SciPostPhysCore.6.3.050
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Abstract

We construct a symbol and coaction for the $l$-loop sunrise family of integrals, both for 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 these integrals in a unipotent form. We augment the 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, and its connection to notions of transcendental weight.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.6.3.050
TI  - A symbol and coaction for higher-loop sunrise integrals
PY  - 2023/07/12
UR  - https://www.scipost.org/SciPostPhysCore.6.3.050
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 6
IS  - 3
SP  - 050
A1  - Forum, Andreas
AU  - von Hippel, Matt
AB  - We construct a symbol and coaction for the $l$-loop sunrise family of integrals, both for 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 these integrals in a unipotent form. We augment the 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, and its connection to notions of transcendental weight.
ER  -

@Article{10.21468/SciPostPhysCore.6.3.050,
	title={{A symbol and coaction for higher-loop sunrise integrals}},
	author={Andreas Forum and Matt von Hippel},
	journal={SciPost Phys. Core},
	volume={6},
	pages={050},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.6.3.050},
	url={https://scipost.org/10.21468/SciPostPhysCore.6.3.050},
}

Cited by 3

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¹ Andreas Forum,
¹ Matt von Hippel

¹ Niels Bohr Institute [NBI]

Funders for the research work leading to this publication