Fixed Point Resolution in Extensions of Permutation Orbifolds

TL;DR

This paper analyzes fixed point resolution in permutation orbifolds, detailing how simple currents and fixed points are determined and resolved, with explicit examples for specific models like SU(2)_k and series B(n)_1, D(n)_1.

Contribution

It provides a systematic method for identifying simple currents and fixed points in orbifold theories and explicitly computes the fixed point resolution matrices for key models.

Findings

Determined simple currents and fixed points for orbifold theories.

Computed fixed point resolution matrices for SU(2)_2, B(n)_1, D(n)_1 series.

Illustrated the process with detailed examples for specific models.

Abstract

We determine the simple currents and fixed points of the orbifold theory $CFT\otimes CFT/\mathbb{Z}_2$, given the simple currents and fixed point of the original $CFT$. We see in detail how this works for the $SU(2)_k$ WZW model, focusing on the field content (i.e. $h$-spectrum of the primary fields) of the theory. We also look at the fixed point resolution of the simple current extended orbifold theory and determine the $S^J$ matrices associated to each simple current for $SU(2)_2$ and for the $B(n)_1$ and $D(n)_1$ series.