Special Fano geometry from Feynman integrals

Abstract

One of the fundamental open questions in QFT is what kind of functions appear as Feynman integrals. In recent years this question has often been considered in a geometric context by interpreting the polynomials that appear in these integrals as defining algebraic varieties. One focal point of the past decade has in particular been the class of Calabi-Yau varieties that arise in some types of Feynman integrals. A class of manifolds that includes CYs as a special case are varieties of special Fano types. These varieties were originally introduced because the class of CY spaces is not closed under mirror symmetry. Their Hodge structure is of a more general type and the middle cohomology in particular is determined by two integers, the dimension of the manifold and a charge $Q$. In the present paper this class of manifolds is considered in the context of Feynman integrals.

23 pages, 5 figures