Fermionic and parafermionic CFTs with $\widehat{su}(2)$ and $\widehat{su}(3)$ symmetry

TL;DR

This paper extends the classification of two-dimensional conformal field theories with affine $\\widehat{su}(2)$ and $\\widehat{su}(3)$ symmetries to include fermionic and parafermionic models, revealing connections to non-simply laced Dynkin diagrams.

Contribution

It introduces a classification of fermionic and parafermionic CFTs with affine symmetries, expanding beyond previously known bosonic models using fermionization techniques.

Findings

Fermionic and parafermionic models relate to non-simply laced Dynkin diagrams.

Complete classification of these models with affine symmetries.

Extension of ADE classification to include fermionic and parafermionic theories.

Abstract

We investigate two-dimensional conformal field theories (CFTs) with affine $\widehat{su}(2)$ and $\widehat{su}(3)$ algebra symmetry. Their bosonic modular-invariant partition functions have been fully classified based on the ADE classification. In this work, we extend the classification to include fermionic and parafermionic CFTs with the same affine symmetries, utilizing techniques of fermionization and parafermionization. We find that the fermionic and parafermionic $\widehat{su}(2)$ models are related to non-simply laced Dynkin diagrams.