Humboldt University, Berlin

In this talk I review the recent discovery of Yangian symmetry for massive Feynman integrals and how it can be used to set up a Yangian Bootstrap. I will provide elementary proofs of the symmetry at one and two loops, whereas at generic loop order I conjecture that all graphs cut from regular tilings of the plane with massive propagators on the boundary enjoy the symmetry. After demonstrating how the symmetry may be used to constrain the functional form of Feynman integrals on explicit examples, I comment on how a subset of the diagrams for which the symmetry is conjectured to hold is naturally embedded in a Massive Fishnet theory that descends from gamma-deformed Coulomb branch N=4 Super-Yang-Mills theory in a particular double scaling limit.

Abstract: Hairer recently had the remarkable insight that Lyons' theory of rough paths can be used to make sense of nonlinear SPDEs that were previously ill-defined due to spatial irregularities. Since rough path theory deals with the integration of functions defined on the real line, the SPDEs studied by Hairer have a one-dimensional spatial index variable. I will show how to combine paraproducts, a notion from functional analysis, with ideas from the theory of controlled rough paths, in order to develop a formulation of rough path theory that works in any index dimension. As an application, I will present existence and uniqueness results for an SPDE with multidimensional spatial index set, for which previously it was not known how to describe solutions. No prior knowledge of rough paths or paraproducts is required for understanding the talk. This is joint work with Massimiliano Gubinelli and Peter Imkeller.