IAS Amplitudes Group Meeting

Abstract: Over the last few years, much has been learned about the types of special functions that Feynman diagrams give rise to near integer dimensions. In this talk, I further explore this question by studying a new infinite class of planar Feynman diagrams, which can be constructed by sequentially intersecting so-called traintrack diagrams. After describing how to derive a 2L-fold integral representation of any L-loop diagram in this class, I will show that these diagrams always give rise to integrals over (L−1)-dimensional varieties for generic external momenta. I will then go on to demonstrate that (products of) these diagrams are related at adjacent loop orders by a large class of second-order differential operators, whose number grows linearly with L and which can be used to recursively expose much of the analytic structure exhibited by these diagrams.