Speaker
Description
The Feynman integral is a complicated analytic function in many variables, associated to a merely combinatorial object, namely a graph. In this talk I will focus on the highest order poles of the Feynman integral, and explain how they can be described entirely by combinatorics of the graph. In fact, we conjecture that the integral itself is fully determined by these residues, which turn out to be products of the tropical limit of the integral (Hepp bound) and the diagonal coefficients of the integrand. This perspective opens up the possibility to prove identities of integrals purely by combinatorics.
I will illustrate these ideas concretely with periods in phi^4 theory, where by another miracle the combinatorics of spanning trees is related to circuit partitions, which allows for efficient recursive computations. In this context, I illustrate a conjecture that Euler-Mellin integrals (at integer Mellin arguments) are Apery-like limits of recurrence relations (similar to the construction in Apery’s proof of the irrationality of zeta(3)).
This talk covers past work with Karen Yeats (arXiv:2304.05299) and ongoing work with Francis Brown.
