Extended Operator Algebra and Reducibility in the WZW Permutation Orbifolds

TL;DR

This paper extends the operator algebra and Virasoro structures in WZW permutation orbifolds, simplifies the twisted KZ equations, and analyzes the spectrum, providing deeper understanding of their algebraic and spectral properties.

Contribution

It introduces an extended orbifold Virasoro algebra and simplifies the twisted KZ equations for WZW permutation orbifolds, advancing the algebraic framework and spectral analysis.

Findings

Extended orbifold Virasoro algebra for WZW permutation orbifolds

Simplified single-cycle twisted KZ equations

Identified principal primary states and fields in the spectrum

Abstract

Recently the operator algebra, including the twisted affine primary fields, and a set of twisted KZ equations were given for the WZW permutation orbifolds. In the first part of this paper we extend this operator algebra to include the so-called orbifold Virasoro algebra of each WZW permutation orbifold. These algebras generalize the orbifold Virasoro algebras (twisted Virasoro operators) found some years ago in the cyclic permutation orbifolds. In the second part, we discuss the reducibility of the twisted affine primary fields of the WZW permutation orbifolds, obtaining a simpler set of single-cycle twisted KZ equations. Finally we combine the orbifold Virasoro algebra and the single-cycle twisted KZ equations to investigate the spectrum of each orbifold, identifying the analogues of the principal primary states and fields also seen earlier in cyclic permutation orbifolds. Some remarks about general WZW orbifolds are also included.