On the operator content of nilpotent orbifold models

Chongying Dong; Geoffrey Mason

paper

On the operator content of nilpotent orbifold models

arXiv:hep-th/9412109

Abstract

Let $V$ be a simple vertex operator algebra and $G$ be a finite nilpotent group of automorphisms of $V .$ We prove the following in this paper: (1) There is a Galois correspondence between subgroups of $G$ and the vertex operator subalgebras of $V$ which contain $V^{G}$ given by the map $H \mapsto V^{H} .$ (2) Assume that for every G\in G $t h er e i s u ni q u es im pl e$ g $- tw i s t e d$ V $- m o d u l e$ M(g). $T h e n t h er ee x i s t s a H oc h sc hi l d 3 - cocy c l e$ α $o n t h e in t e g r a l g r o u p$ Z[G] $s u c h t ha tt h er e i s an e q u i v a l e n ceo f c a t e g or i es b e tw ee n$ V^G $- m o d u l ec a t e g or y (w h oseo bj ec t s a r e$ V^G $- s u bm o d u l eso f d i r ec t s u m so f co p i eso f$ \oplus_{g\in G}M(g), $an d w h ose m or p hi s m s a r e$ V^G $- m o d u l e h o m o m or p hi s m s) an d t h e m o d u l ec a t e g or y f or t h e tw i s t e d q u an t u m d o u b l e$ D_α(G) $a ssoc ia t e d t o$ α.$

26 pages, Latex

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On quantum Galois theory

On the operator content of nilpotent orbifold models

Abstract

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