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.