Macaulay matrix for Feynman integrals: linear relations and intersection numbers
Vsevolod Chestnov, Federico Gasparotto, Manoj Kumar Mandal, Pierpaolo Mastrolia, Saiei-Jaeyeong Matsubara-Heo, Henrik J. Munch, Nobuki Takayama · Journal of High Energy Physics · 2022
A bstract 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 $$ \mathcal{A} $$ A -hypergeometric (Euler) integrals and Feynman integrals, through recurrence relations and through projections by intersection numbers.