Polytope symmetries of Feynman integrals

Abstract

Feynman integrals appropriately generalized are A-hypergeometric functions. Among the properties of A-hypergeometric functions are symmetries associated with the Newton polytope. In ordinary hypergeometric functions these symmetries lead to linear transformations. Combining tools of A-hypergeometric systems and the computation of symmetries of polytopes, we consider the associated symmetries of Feynman integrals in the Lee-Pomeransky representation. We compute the symmetries of n-gon integrals up to n=8, massive banana integrals up to 5-loop, and on-shell ladders up to 3-loop. We apply these symmetries to study finite on-shell ladder integrals up to 3-loop.