A Bestiary of Feynman Integral Calabi-Yaus

by Matt von Hippel (Niels Bohr Institute)

Friday 12 Mar 2021, 11:00 → 12:00 Europe/Berlin

While the simplest Feynman diagrams evaluate to multiple polylogarithms, more complicated functions can arise, involving integrals over higher-dimensional manifolds. Surprisingly, all examples of such manifolds in the literature to date are Calabi-Yau. I discuss why this is, and prove that a specific class of "marginal" diagrams give rise to Calabi-Yau manifolds. I demonstrate a bound on the dimensionality of these manifolds with loop order, and present infinite families of diagrams that saturate this bound to all orders. Finally, I discuss some integrals that don't fit this picture and still need a good explanation.

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