Description
Abstract: Feynman integrals are related through linear relations, often called Integration-By-Parts relations, or IBPs for short.
Usually IBPs relate integrals in a generating sector, with integrals in its subsectors. It can, however, happen that the integrals in the generating sector drop out, and the IBP relates subsector integrals only, and that type of IBPs are known as magic relations. Magic relations are of interest, since they cause problems for cut-based approaches to IBP reduction, as well as to intersection theory in the framework of relative twisted cohomology.
The main result of this presentation, and of the paper on which it is based, is the discovery that magic relations always come together with a generating sector that has a higher dimensional critical variety.
We also outline a proof of this result, discuss how to count master integrals in the presence of higher dimensional critical varieties (using Morse-Bott theory), and discuss how magic relations interact with symmetry relations.