Discrete symmetries of unitary minimal conformal theories Original Research Article

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 Z2 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 S3 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.