2002/08/31 by M. B. Halpern, M. B. HALPERN, C. Helfgott +1
Mathematics · Physics and Astronomy · #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Current algebra #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Operator (biology) #Operator algebra #Orbifold #Permutation (music) #Superconformal algebra #Virasoro algebra #hep-th
paper · pdf · doi:10.1142/s0217751x03013971
published as Int.J.Mod.Phys.A18:1773-1826,2003 · 57 pages, typos fixed
arxiv created 2003/02/25 · openalex publication_date 2003/04/11 · arxiv updated 2014/11/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.