New Semiclassical Nonabelian Vertex Operators for Chiral and Nonchiral WZW Theory

We supplement the discussion of Moore and Reshetikhin and others by finding new semiclassical nonabelian vertex operators for the chiral, antichiral and nonchiral primary fields of WZW theory. These new nonabelian vertex operators are the natural generalization of the familiar abelian vertex operators: They involve only the representation matrices of Lie g, the currents of affine (g × g) and certain chiral and antichiral zero modes, and they reduce to the abelian vertex operators in the limit of abelian algebras. Using the new constructions, we also discuss semiclassical operator product expansions, braid relations and relations to the known form of the semiclassical affine-Sugawara conformal blocks. e-mail address: [email protected] Address after Oct. 1, 1996: Theory Division CERN, CH-1211 Geneva 23, Switzerland; e-mail address: [email protected] Laboratoire Propre du CNRS UPR A.0014