The Operator Algebra and Twisted KZ Equations of WZW Orbifolds

TL;DR

This paper derives the operator algebra and twisted KZ equations for all WZW orbifolds, revealing new structures in twisted sectors and providing differential equations for twisted primary fields.

Contribution

It introduces the complete operator algebra for twisted sectors of WZW orbifolds and derives the corresponding twisted KZ equations, including permutation and inner-automorphic cases.

Findings

Twisted right and left mover current algebras are not necessarily identical.

Derived world-sheet differential equations for twisted affine primary fields.

Established twisted Knizhnik-Zamolodchikov equations for various orbifolds.

Abstract

We obtain the operator algebra of each twisted sector of all WZW orbifolds, including the general twisted current algebra and the algebra of the twisted currents with the twisted affine primary fields. Surprisingly, the twisted right and left mover current algebras are not a priori copies of each other. Using the operator algebra we also derive world-sheet differential equations for the twisted affine primary fields of all WZW orbifolds. Finally we include ground state properties to obtain the twisted Knizhnik-Zamolodchikov equations of the WZW permutation orbifolds and the inner-automorphic WZW orbifolds.