# Hexagons and Correlators in the Fishnet Theory

## TL;DR

This paper explores the application of the hexagon formalism to the planar 4d conformal fishnet theory, deriving form factors and validating them through correlator calculations and renormalization tests.

## Contribution

It derives hexagon form factors for the fishnet theory and demonstrates their use in computing correlators, connecting integrability with explicit Feynman diagram results.

## Key findings

- Successful derivation of hexagon form factors for various states.
- Agreement between hexagon-based calculations and Feynman diagram results.
- Validation of the renormalization procedure at higher orders.

## Abstract

We investigate the hexagon formalism in the planar 4d conformal fishnet theory. This theory arises from N=4 SYM by a deformation that preserves both conformal symmetry and integrability. Based on this relation, we obtain the hexagon form factors for a large class of states, including the BMN vacuum, some excited states, and the Lagrangian density. We apply these form factors to the computation of several correlators and match the results with direct Feynman diagrammatic calculations. We also study the renormalisation of the hexagon form factor expansion for a family of diagonal structure constants and test the procedure at higher orders through comparison with a known universal formula for the Lagrangian insertion.