Numerical evidence for a Haagerup conformal field theory

TL;DR

This paper provides numerical evidence that an anyon chain based on the Haagerup fusion category exhibits a conformal field theory with a central charge around 2, representing a novel example of exotic generalized symmetries.

Contribution

It is the first to numerically demonstrate a conformal field theory arising from the Haagerup fusion category, showcasing truly exotic non-invertible symmetries.

Findings

Evidence of a conformal field theory with central charge ~2

First example of CFT with Haagerup fusion category symmetry

Demonstrates existence of exotic generalized symmetries in CFTs

Abstract

We numerically study an anyon chain based on the Haagerup fusion category, and find evidence that it leads in the long-distance limit to a conformal field theory whose central charge is $\sim 2$. Fusion categories generalize the concept of finite group symmetries to non-invertible symmetry operations, and the Haagerup fusion category is the simplest one which comes neither from finite groups nor affine Lie algebras. As such, ours is the first example of conformal field theories which have truly exotic generalized symmetries.