Joint Theory Seminar: Christoph Nega

Speaker: Christoph Nega

Title: Calabi-Yau Manifolds and Feynman Integrals — The Family of Banana Graphs

Abstract:
In this talk I will explain the relation between Calabi-Yau manifolds and their mathematics and Feynman integral computations. We will see how concepts from Calabi-Yau geometries and especially Calabi-Yau motives can be used to compute multi-loop Feynman integrals. This will be exemplified with the so called banana graphs. First, I will give a short introduction to Feynman integrals and Calabi-Yau manifolds. Then we will see how the mathematics of Calabi-Yau manifolds (variations of Hodge structures, Griffiths transversality, Gammaclass, ...) constrain or even determine the corresponding Feynman integrals, here the banana graphs. Then I will also shortly explain how the banana integrals can be solved in dimensional regularization in the equal- as well as in the generic-mass case. Finally, I will make some remarks what we can in general learn from Calabi-Yau spaces in the context of Feynman integrals.