1994/07/31 by Matthias R. Gaberdiel, M. R. Gaberdiel · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Quantum Mechanics and Non-Hermitian Physics #hep-th
paper · pdf · doi:10.1007/bf02101238
published as Commun.Math.Phys. 173 (1995) 357-378 · 28 pages, LATEX; a remark about other possible symmetry algebras and some references are added
arxiv created 1995/05/22 · openalex publication_date 1995/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
It is shown how a chiral Wess-Zumino-Witten theory with globally defined vertex operators and a one-to-one correspondence between fields and states can be constructed. The Hilbert space of this theory is the direct sum of tensor products of representations of the chiral algebra and finite dimensional internal parameter spaces. On this enlarged space there exists a natural action of Drinfeld's quasi quantum group Ag,t, which commutes with the action of the chiral algebra and plays the rôle of an internal symmetry algebra. The R matrix describes the braiding of the chiral vertex operators and the coassociator Φ gives rise to a modification of the duality property. For generic q the quasi quantum group is isomorphic to the coassociative quantum group Uq(g) and thus the duality property of the chiral theory can be restored. This construction has to be modified for the physically relevant case of integer level. The quantum group has to be replaced by the corresponding truncated quasi quantum group, which is not coassociative because of the truncation. This exhibits the truncated quantum group as the internal symmetry algebra of the chiral WZW model, which therefore has only a modified duality property. The case of g=su(2) is worked out in detail.