Simple Current Actions of Cyclic Groups

TL;DR

This paper investigates permutation actions of simple currents in Rational Conformal Field Theories, providing a classification for cyclic groups and describing how primaries form multiplets based on simple current properties.

Contribution

It offers a complete solution to admissibility conditions for cyclic quadratic groups and characterizes the arrangement of primaries into specific multiplets.

Findings

Primaries form multiplets of length k^2 or 3k^2 depending on simple current spin.

Each subgroup of the quadratic group corresponds to an irreducible weighted permutation action.

The classification applies to simple currents with integral or half-integral spin.

Abstract

Permutation actions of simple currents on the primaries of a Rational Conformal Field Theory are considered in the framework of admissible weighted permutation actions. The solution of admissibility conditions is presented for cyclic quadratic groups: an irreducible WPA corresponds to each subgroup of the quadratic group. As a consequence, the primaries of a RCFT with an order n integral or half-integral spin simple current may be arranged into multiplets of length k^2 (where k is a divisor of n) or 3k^2 if the spin of the simple current is half-integral and k is odd.