Title: Combinatorial proof of a Non-Renormalization Theorem
| Speaker: | Paul Balduf |
| Affiliation: | University of Waterloo |
| Location: | MC 5479 |
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm.
Abstract: In "Higher Operations in Perturbation Theory", Gaiotto, Kulp, and Wu discussed Feynman integrals that controls certain deformations in quantum field theory. These integrals themselves are differential forms, and the authors conjectured that one class of them squares to zero. This phenomenon can be interpreted as absence of quantum corrections in topological quantum field theories with more than one topological direction, or as an analogue of Kontsevich's formality theorem. In my talk, I will present a purely combinatorial proof of the conjecture for arbitrary graphs. It is based on graph matrices and graph polynomials, and a careful analysis of the involved signs and multiplicities. No knowledge or intution of the underlying physics is required.
In the preseminar, I will review the necessary definitions and properties of graph polynomials, and how they are typically applied in Feynman integrals. If time permits, I might also comment on the physical background.