MODULAR INVARIANCE IN S3 SYMMETRIC 2D CONFORMAL FIELD THEORIES

Abstract

Using GKO construction, we conjecture a formula for the characters of highest weight irreducible representations of the algebra of conformal models having S3 symmetry with spin 4/3 parafermionic currents constructed by Fateev and Zamolodchikov. The modular transformations of these characters are given and modular invariant partition functions are classified. It turns out that an A-D-E classification similar to that found in conformal and N=1 superconformal theories holds. For the particular case of the tricritical 3-state Potts model the connection with Virasoro characters is given.