Two Large Examples in Orbifold Theory: Abelian Orbifolds and the Charge Conjugation Orbifold on su(n)

TL;DR

This paper presents two extensive examples in orbifold theory, solving twisted vertex operator equations for abelian orbifolds and deriving twisted KZ equations for the charge conjugation orbifold on su(n), expanding the understanding of orbifold models.

Contribution

It provides explicit solutions for twisted vertex operators in abelian orbifolds and formulates twisted KZ equations for the charge conjugation orbifold on su(n), advancing orbifold theory.

Findings

Explicit twisted vertex operators for abelian orbifolds

Twisted KZ equations for charge conjugation orbifold on su(n)

Enhanced understanding of orbifold operator algebra

Abstract

Recently the operator algebra and twisted vertex operator equations were given for each sector of all WZW orbifolds, and a set of twisted KZ equations for the WZW permutation orbifolds were worked out as a large example. In this companion paper we report two further large examples of this development. In the first example we solve the twisted vertex operator equations in an abelian limit to obtain the twisted vertex operators and correlators of a large class of abelian orbifolds. In the second example, the twisted vertex operator equations are applied to obtain a set of twisted KZ equations for the (outer-automorphic) charge conjugation orbifold on su(n \geq 3).