Scaling fields in the two-dimensional abelian sandpile model

TL;DR

This paper connects the two-dimensional abelian sandpile model to conformal field theory, demonstrating that its scaling limit aligns with a c=-2 conformal field theory and its massive perturbation, confirming conformal invariance.

Contribution

It provides the first direct evidence linking the sandpile model's scaling limit to a specific conformal field theory, using lattice correlation functions.

Findings

Correlation functions match c=-2 conformal field theory predictions

Evidence supports conformal invariance in the model's scaling limit

Analysis of height variables remains inconclusive

Abstract

We consider the isotropic two-dimensional abelian sandpile model from a perspective based on two-dimensional (conformal) field theory. We compute lattice correlation functions for various cluster variables (at and off criticality), from which we infer the field-theoretic description in the scaling limit. We find a perfect agreement with the predictions of a c=-2 conformal field theory and its massive perturbation, thereby providing direct evidence for conformal invariance and more generally for a description in terms of a local field theory. The question of the height 2 variable is also addressed, with however no definite conclusion yet.