Coset Realization of Unifying W-Algebras

Details Coset Realization of Unifying W-Algebras Coset Realization of Unifying W-Algebras

1994-06-30

arxiv.org/abs/hep-th/9406203v2

Int.J.Mod.Phys. A10 (1995) 2367-2430

Physics

High Energy Physics

High Energy Physics - Theory

60 pages (plain TeX) (final version to appear in Int. J. Mod. Phys. A; several minor improvements and corrections - for detail

Scientific paper

10.1142/S0217751X95001157

We construct several quantum coset W-algebras, e.g. sl(2,R)/U(1) and sl(2,R)+sl(2,R) / sl(2,R), and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying W-algebras of Casimir W-algebras. We show that it is possible to give coset realizations of various types of unifying W-algebras, e.g. the diagonal cosets based on the symplectic Lie algebras sp(2n) realize the unifying W-algebras which have previously been introduced as `WD_{-n}'. In addition, minimal models of WD_{-n} are studied. The coset realizations provide a generalization of level-rank-duality of dual coset pairs. As further examples of finitely nonfreely generated quantum W-algebras we discuss orbifolding of W-algebras which on the quantum level has different properties than in the classical case. We demonstrate in some examples that the classical limit according to Bowcock and Watts of these nonfreely finitely generated quantum W-algebras probably yields infinitely nonfreely generated classical W-algebras.

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