Discrete symmetries of unitary minimal conformal theories

TL;DR

This paper classifies the discrete symmetries of two-dimensional unitary minimal conformal theories, revealing that most have Z_2 symmetry, with exceptions including models with S_3 symmetry and some with no symmetry.

Contribution

It provides a comprehensive classification of discrete symmetries in unitary minimal conformal models, linking them to Lie algebra automorphisms and analyzing symmetry preservation in sectors.

Findings

Most models have Z_2 symmetry as maximal.

Six models are exceptions: four with no symmetry, two with S_3 symmetry.

Symmetries match automorphism groups of ADE Dynkin diagrams.

Abstract

We classify the possible discrete (finite) symmetries of two--dimensional critical models described by unitary minimal conformally invariant theories. We find that all but six models have the group Z_2 as maximal symmetry. Among the six exceptional theories, four have no symmetry at all, while the other two are the familiar critical and tricritical 3--Potts models, which both have an S_3 symmetry. These symmetries are the expected ones, and coincide with the automorphism groups of the Dynkin diagrams of simply--laced simple Lie algebras ADE. We note that extended chiral algebras, when present, are almost never preserved in the frustrated sectors.