Fishnet Integrals from Integrability and Geometry

by Dr Florian Loebbert (University of Bonn)

Thursday 24 Nov 2022, 15:00 → 17:00 Europe/Berlin

SR2 (Building 2a)

Abstract:

The computation of Feynman integrals still represents a
bottle neck for precision calculations in quantum field theory.
Recent progress goes hand in hand with the understanding of new
function classes and their mathematical structure. In this talk
we discuss the so-called fishnet integrals that represent an
infinite family of scalar Feynman integrals featuring integrable
structures. In particular we review the Yangian quantum group
symmetry of these integrals which extends the conformal spacetime
symmetry of the associated fishnet quantum field theories. We
then focus on the specific case of fishnets in two spacetime
dimensions and argue that these integrals compute the quantum
volumes of Calabi-Yau varieties. Here the Yangian provides a
convenient tool that yields the Picard-Fuchs differential
equations for the Calabi-Yau periods, while the geometry dictates
the particular linear combination of periods, which furnishes the
Feynman integrals.

 

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Meeting ID: 645 5999 3590
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