Speaker: Tobias Scherdin (HU Berlin)

Title: Yangian Differential Equations for Polygonic Feynman Integrals

Abstract:
Yangian symmetry puts constraints on certain dual conformal invariant Feynman integrals. Those integrals are, for example, featured in N=4 SYM, where the Yangian is closely tied to the integrability of the theory. In general, those constraints can be written as second-order differential equations that the integrals must obey.
In this talk, we will focus on the 1-loop case, i.e. n-gons in n dimensions. Those integrals are of multipolylogarithmic type, as we will see explicitly for the simplest examples of the box and pentagon integrals. We then argue for a certain choice of variables, in which we can consider the general n-gon in n dimensions and derive its Yangian differential equations.
Even though 1-loop integrals only pose the simplest non-trivial scenario, a deep understanding of them is important for higher loop orders as well, as there are various connections between n-gons in n dimensions and higher-loop integrals.