Christoph Nega (Bonn): Analytic Structure of Banana Feynman Integrals

In this talk I will introduce the so called banana Feynman integrals and explain their analytic properties in dimensional regularization.
These Feynman integrals have a natural interpretation as relative periods of a complete intersection Calabi-Yau manifold, whose dimension is the loop order minus one of the banana integral.
In particular, we find that the leading logarithmic structure in the high energy regime, which corresponds to the point of maximal unipotent monodromy, is determined by a novel Gamma-class evaluation in the ambient space of the mirror CY and the mirror CY itself.
Moreover, we provide simple closed all loop formulas for the Frobenius kappa-constants at the physical threshold in terms of zeta values.
I will also give a short outlook how the above structures evolve in the expansion in the dimensional regularization parameter.
Finally, I comment on the situation in the non-equal mass case.