Nonabelian Toda Theories from Parafermionic Reductions of the WZW Model
✍ Scribed by J.F. Gomes; G.M. Sotkov; A.H. Zimerman
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 477 KB
- Volume
- 274
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
We investigate a class of conformal nonabelian-Toda models representing noncompact SL(2, R)ÂU(1) parafermions (PF) interacting with specific abelian Toda theories and having a global U(1) symmetry. A systematic derivation of the conserved currents, their algebras, and the exact solution of these models are presented. An important property of this class of models is the affine SL(2, R) q algebra spanned by charges of the chiral and antichiral nonlocal currents and the U(1) charge. The classical (Poisson brackets) algebras of symmetries VG n of these models appear to be of mixed PF-WG n type. They contain together with the local quadratic terms specific for the W n -algebras the nonlocal terms similar to the ones of the classical PF-algebra. The renormalization of the spins of the nonlocal currents is the main new feature of the quantum VA n -algebras. The quantum VA 2 -algebra and its degenerate representations are studied in detail.