Integrability for Feynman Integrals

TL;DR

This paper explores the Yangian symmetry in Feynman integrals, highlighting integrability structures emerging from the fishnet limit of AdS/CFT, and discusses their implications for differential equations and geometric interpretations.

Contribution

It introduces the Yangian symmetry framework for Feynman integrals, extending integrability concepts to various propagator masses and dimensions, and connects to geometric invariants.

Findings

Yangian differential equations for massless fishnets in 4D

Extension to massive propagators and arbitrary dimensions

Identification of Yangian invariants with Calabi-Yau period 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.