IngentaConnect Chiral zero modes of the SU(n) Wess-Zumino-Novikov-Witten model

Authors: Furlan P.¹; Hadjiivanov L.K.¹; Todorov I.T.²

Source: Journal of Physics A: Mathematical and General, Volume 36, Number 13, 2003 , pp. 3855-3875(21)

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Abstract:

We define the chiral zero modes' phase space of the GSU(n) Wess-Zumino-Novikov-Witten (WZNW) model as an (n - 1)(n + 2)-dimensional manifold _q equipped with a symplectic form _q involving a Wess-Zumino term which depends on the monodromy M and is implicitly defined (on an open dense neighbourhood of the group unit) by

This classical system exhibits a Poisson-Lie symmetry that evolves upon quantization into a Uq(s_n) symmetry for q a primitive even root of 1. For each (non-degenerate, constant) solution of the classical Yang-Baxter equation we write down explicitly a (M) satisfying equation ( lowast ) and invert the form _q, thus computing the Poisson bivector of the system. The resulting Poisson brackets (PB) appear as the classical counterpart of the exchange relations of the quantum matrix algebra studied previously in Furlan et al (2000 Preprint hep-th/0003210). We argue that it is advantageous to equate the determinant D of the zero modes' matrix (aj) to a pseudoinvariant under permutations q-polynomial in the SU(n) weights, rather than to adopt the familiar convention D 1. A finite-dimensional 'Fock space' operator realization of the factor algebra _q/_h where _h is an appropriate ideal in _q for qh -1, is briefly discussed.

Language: English

Document Type: Miscellaneous

Affiliations: 1: Dipartimento di Fisica Teorica dell' Università degli Studi di Trieste, Strada Costiera 11, I-34014 Trieste, Italy 2: Theoretical Physics Division, Institute for Nuclear Research and Nuclear Energy, Tsarigradsko Chaussee 72, BG-1784 Sofia, Bulgaria