HEP Theory Journal Club

On the Poincare dual of Feynman integrals

Andrzej Pokraka

McGill

Recently it has been shown that integration by parts (IBP) coefficients for Feynman integrals can be obtained from intersection numbers of the corresponding twisted cohomology classes in a completely algebraic manner. However, Feynman integrals violate certain generality conditions and must be regularized in the traditional approach. This regularization introduces extra parameters increasing the complexity of intersection number computations.

We lift the generality conditions, removing the need for regulation, by study Feynman integrals in the framework of relative-twisted cohomology. We argue that cohomology classes dual to Feynman integrals are, in fact, much simpler than their counterparts. These dual forms have support only on propagator cuts localizing intersection numbers to the cut surfaces. This makes defining an orthogonal basis of the cohomology easy to construct and therefore the intersection with a dual form directly computes the corresponding IPB coefficient.