Gluing Ladders into Fishnets

Abstract

We use integrability at weak coupling to compute fishnet diagrams for four-point correlation functions in planar $ϕ^4$ theory. The results are always multi-linear combinations of ladder integrals, which are in turn built out of classical polylogarithms. The Steinmann relations provide a powerful constraint on such linear combinations, leading to a natural conjecture for any fishnet diagram as the determinant of a matrix of ladder integrals.

6 pages, 4 figures; v2, minor corrrections, e.g. in fig. 2 caption