Extended Operator Algebra and Reducibility in the WZW Permutation Orbifolds

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.

57 pages, typos fixed

References in corpus (2)

• Two Large Examples in Orbifold Theory: Abelian Orbifolds and the Charge Conjugation Orbifold on su(n)
• The General Coset Orbifold Action

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• A Basic Class of Twisted Open WZW Strings
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26. I.Extended Actions and New Twisted World-Sheet Gravities
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26 IV. Orientation Orbifolds Include Orientifolds
• The Orbifold-String Theories of Permutation-Type: I. One Twisted BRST per Cycle per Sector
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26 II. The Twisted BRST Systems of \hatc=52 Matter
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of $c=26$ III. The Spectra of $\hat{c}=52$ Strings
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of $\mathbf{c}=26$ V. Cyclic Permutation Orbifolds
• The orbifold-string theories of permutation-type: II. Cycle dynamics and target space-time dimensions
• The Orbifold-String Theories of Permutation-Type: III. Lorentzian and Euclidean Space-Times in a Large Example