# Gluing Ladders into Fishnets

## TL;DR

This paper employs integrability techniques to compute fishnet diagrams in planar phi^4 theory, revealing their structure as determinants of ladder integrals constrained by Steinmann relations.

## Contribution

It introduces a novel approach to express fishnet diagrams as determinants of ladder integrals, guided by Steinmann relations, advancing the understanding of correlation functions in planar phi^4 theory.

## Key findings

- Fishnet diagrams are multi-linear combinations of ladder integrals.
- Ladder integrals are expressed using classical polylogarithms.
- Steinmann relations constrain the form of fishnet diagrams.

## Abstract

We use integrability at weak coupling to compute fishnet diagrams for four-point correlation functions in planar $\phi^4$ 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.