Dualities between fermionic theories and the Potts model

TL;DR

This paper establishes a duality between a broad class of fermionic theories and a limit of the Potts model, using a random forest representation, and applies this to describe certain invariant field theories with sigma model UV completions.

Contribution

It introduces a duality framework connecting fermionic theories to Potts models via random forests and applies it to invariant field theories with sigma model UV completions.

Findings

Fermionic theories are dual to a $q o 0$ limit of the Potts model with magnetic field.

Random forest models generalize the Potts model description.

Provides a statistical description of $OSp(1|2M)$ invariant field theories.

Abstract

We show that a large class of fermionic theories are dual to a $q \to 0$ limit of the Potts model in the presence of a magnetic field. These can be described using a statistical model of random forests on a graph, generalizing the (unrooted) random forest description of the Potts model with only nearest neighbor interactions. We then apply this to find a statistical description of a recently introduced family of $OSp(1|2M)$ invariant field theories that provide a UV completion to sigma models with the same symmetry.