# Three-point functions in the fully packed loop model on the honeycomb lattice

## TL;DR

This paper investigates three-point functions in the Fully-Packed Loop model on the honeycomb lattice, combining analytical Coulomb-Gas theory with numerical transfer-matrix methods to reveal a connection with imaginary Liouville theory.

## Contribution

It introduces a family of three-point correlation functions probing the imaginary Liouville component and provides numerical validation of the theoretical predictions.

## Key findings

- Good agreement between numerical and analytical results
- Universal amplitudes and spatial dependence confirmed
- Relation between loop models and imaginary Liouville theory is likely general

## Abstract

The Fully-Packed Loop (FPL) model on the honeycomb lattice is a critical model of non-intersecting polygons covering the full lattice, and was introduced by Reshetikhin in 1991. Using the two-component Coulomb-Gas approach of Kondev, de Gier and Nienhuis (1996), we argue that the scaling limit consists of two degrees of freedom: a field governed by the imaginary Liouville action, and a free boson. We introduce a family of three-point correlation functions which probe the imaginary Liouville component, and we use transfer-matrix numerical diagonalisation to compute finite-size estimates. We obtain good agreement with our analytical predictions for the universal amplitudes and spatial dependence of these correlation functions. Finally we conjecture that this relation between non-intersecting loop models and the imaginary Liouville theory is in fact quite generic. We give numerical evidence that this relation indeed holds for various loop models.