Integrability for Feynman Integrals

by Florian Löbbert (Bonn)

HS2 (Physikdepartment)




Feynman integrals are crucial ingredients for calculations within quantum field theory. A new tool for their investigation comes with the recent discovery of integrable structures for large families of Feynman graphs and the associated symmetry constraints. These constraints can be formulated in terms of the Yangian algebra and result in differential equations for the considered integrals. Here we review the Yangian symmetry of Feynman integrals and its connection to AdS/CFT integrability via the so-called fishnet theories. We demonstrate how to bootstrap Feynman integrals using these constraints and discuss the recent relation between Yangian symmetry and Calabi-Yau geometry for integrals in two spacetime dimensions. Finally we comment on ideas to extend these approaches to more general classes of Feynman integrals.