Journal of High Energy Physics (Sep 2022)
Macaulay matrix for Feynman integrals: linear relations and intersection numbers
Abstract
Abstract We elaborate on the connection between Gel’fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman Integrals. We propose a novel, more efficient algorithm to compute Macaulay matrices, which are used to derive Pfaffian systems of differential equations. The Pfaffian matrices are then employed to obtain linear relations for A $$ \mathcal{A} $$ -hypergeometric (Euler) integrals and Feynman integrals, through recurrence relations and through projections by intersection numbers.
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