Operator quantization of constrained WZNW theories and coset constructions. A.V.Bratchikov

Operator quantization of constrained WZNW theories and coset constructions. Abstract Using two WZNW theories for Lie algebras g and h, h ⊂ g, we construct the associative quotient algebra which includes a class of g/h coset primary fields and currents. 1. In a recent article [1] for generic g/h coset conformal field theory [2] a class of Virasoro primary fields and currents was constructed.They are explicitly expressed in terms of two Wess-Zumino-Novikov-Witten (WZNW) theories [3, 4] for Lie algebras g and h ⊂ g. It turns out that these fields satisfy the usual definition of primary fields only in the weak sense, i.e. inside correlation functions. The object of this paper is to show that outside correlation functions the primary fields can be represented by elements of an associative quotient algebra Ω/Υ. Since coset fields take values in a quotient algebra, the g/h theory is gauge invariant.The gauge transformations are generated by the ideal Υ. To obtain Ω/Υ we use broken affine primary fields of the WZNW theory for g and an auxiliary WZNW theory for h. Elements of the ideal can be treated as first class constraints and our construction as quantization of the constrained WZNW theory for g ⊕ h. In the case of Abelian cosets this construction was obtained in [5] using a version of the generalized canonical quantization method [6].