Integrability for Feynman integrals

Loebbert, Florian

doi:10.21468/SciPostPhysProc.14.008

SciPost Physics Proceedings

Integrability for Feynman integrals

Florian Loebbert

SciPost Phys. Proc. 14, 008 (2023) · published 23 November 2023

doi: 10.21468/SciPostPhysProc.14.008
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34th International Colloquium on Group Theoretical Methods in Physics

Abstract

We give a brief overview of the Yangian symmetry of Feynman integrals. After a short introduction to the Yangian and integrability, we motivate the emergence of integrable structures for Feynman integrals via the fishnet limit of AdS/CFT. We discuss the resulting Yangian differential equations for massless fishnets in four dimensions as well as generalizations to massive propagators and generic dimensions. We also comment on the relation to momentum space conformal symmetry and on examples in dimensional regularization. Finally we sketch the recent application to fishnet integrals in two spacetime dimensions and the curious identification of Yangian invariants with period integrals of Calabi-Yau geometries.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysProc.14.008
TI  - Integrability for Feynman integrals
PY  - 2023/11/23
UR  - https://scipost.org/SciPostPhysProc.14.008
JF  - SciPost Physics Proceedings
JA  - SciPost Phys. Proc.
VL  - 
IS  - 14
SP  - 008
A1  - Loebbert, Florian
AB  - We give a brief overview of the Yangian symmetry of Feynman integrals. After a short introduction to the Yangian and integrability, we motivate the emergence of integrable structures for Feynman integrals via the fishnet limit of AdS/CFT. We discuss the resulting Yangian differential equations for massless fishnets in four dimensions as well as generalizations to massive propagators and generic dimensions. We also comment on the relation to momentum space conformal symmetry and on examples in dimensional regularization. Finally we sketch the recent application to fishnet integrals in two spacetime dimensions and the curious identification of Yangian invariants with period integrals of Calabi-Yau geometries.
ER  -

@Article{10.21468/SciPostPhysProc.14.008,
	title={{Integrability for Feynman integrals}},
	author={Florian Loebbert},
	journal={SciPost Phys. Proc.},
	pages={008},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysProc.14.008},
	url={https://scipost.org/10.21468/SciPostPhysProc.14.008},
}

Cited by 3

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¹ Florian Loebbert

¹ Rheinische Friedrich-Wilhelms-Universität Bonn / University of Bonn

Funders for the research work leading to this publication

Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
Klaus Tschira Stiftung (through Organization: Klaus Tschira Foundation [KTS])