Quantum gauge group approach to the 2D SU(n) WZNW model

摘要

The canonical quantization of the WZNW model provides a complete set of exchange relations in the enlarged chiral state spaces that include the Gauss components M(sub +-), M-bar(sub +-) of the monodromy matrices M, M-bar. Regarded as new dynamical variables, the elements of M and M-bar cannot be identified; they satisfy different exchange relations. Accordingly, the two dimensional theory expressed in terms of the left and right movers' fields does not automatically respect monodromy invariance. Continuing our recent analysis of the problem by gauge theory methods, we conclude that physical states Phi (on which the field u(x - t)u-bar(x + t) is an element of SU(n) acts as a single valued operator) are invariant under the permuted coproduct of the left and right U(sub q)(sl(n)). They satisfy additional constraints fully described for n = 2; then (i) Phi is invariant under a second U(sub 2)(sl(2)), which commutes with the coproduct, and (ii) (A(sup -))(sup h-1)Phi = 0, where A(sup -)is a quantum group invariant annihilation operator such that (A(sup -))(sup h) = 0 (h = k + 2 being the height). (author). 6 refs. (Atomindex citation 28:028824)