Parafermionic theory with the symmetry Z_5

TL;DR

This paper constructs a Z_5 parafermionic conformal theory based on the Fateev-Zamolodchikov solution, identifying primary operators and their conformal dimensions within a Lie algebra framework.

Contribution

It introduces a new Z_5 parafermionic theory using the second Fateev-Zamolodchikov solution and maps primary operators to the B_2 Lie algebra lattice.

Findings

Primary operators classified as singlet, doublet 1, doublet 2, and disorder operators.

Finite Kac tables for unitary theories are established.

Explicit formula for conformal dimensions of primary operators provided.

Abstract

A parafermionic conformal theory with the symmetry Z_5 is constructed, based on the second solution of Fateev-Zamolodchikov for the corresponding parafermionic chiral algebra. The primary operators of the theory, which are the singlet, doublet 1, doublet 2, and disorder operators, are found to be accommodated by the weight lattice of the classical Lie algebra B_2. The finite Kac tables for unitary theories are defined and the formula for the conformal dimensions of primary operators is given.