Integrability for Feynman Integrals

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.

arXiv comment15 pages, Plenary talk at GROUP34 - The 34th International Colloquium on Group Theoretical Methods in Physics, 18-22 July 2022, Strasbourg, France. Submitted to Scipost Proceedings. v2: references added

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• The thermal representation of conformal ladder integrals
• Hypergeometry from $\hat{\mathrm{P}}$-Symmetry: Feynman Integrals in One and Two Dimensions