New Semiclassical Non-Abelian Vertex Operators for Chiral and Nonchiral WZW Theory

Abstract

We supplement the discussion of Moore and Reshetikhin and others by finding new semiclassical non-Abelian vertex operators for the chiral, antichiral and nonchiral primary fields of WZW theory. These new non-Abelian 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.