New Semiclassical Nonabelian Vertex Operators for Chiral and Nonchiral WZW Theory

TL;DR

This paper introduces new semiclassical nonabelian vertex operators for WZW theory, generalizing abelian operators and connecting to conformal blocks, operator product expansions, and braid relations.

Contribution

It presents the first construction of semiclassical nonabelian vertex operators involving Lie algebra representation matrices and affine currents, extending previous abelian models.

Findings

New nonabelian vertex operators involving Lie algebra matrices and affine currents.

Semiclassical operator product expansions and braid relations derived.

Connections established to affine-Sugawara conformal blocks.

Abstract

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 $(g \times g)$ 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.