From integrability to the Galois coaction on Feynman periods

Abstract

We argue that the description of Feynman loop integrals as integrable systems is intimately connected with their motivic properties and the action of the Cosmic Galois Group. We show how in the case of a family of fishnet graphs, coaction relations between them follow directly from iterative constructions of Q-functions in the quantum spectral curve formalism. Using this observation we conjecture a ``differential equation for numbers'' that enter these periods.

Topics & Concepts