Universal simple current vertex operators

TL;DR

This paper develops a universal vertex operator construction for simple current primary fields in WZW theories based on simply laced affine Lie algebras, using an embedding into bosonic string Fock space.

Contribution

It introduces a universal vertex operator expression applicable across all positive levels for simply laced affine Lie algebras, unifying previous constructions.

Findings

Constructed vertex operators for simple current fields in WZW models.

Unified expression valid for all positive integral levels.

Provides a new algebraic framework for affine Lie algebra representations.

Abstract

We construct a vertex operator realization for the simple current primary fields of WZW theories which are based on simply laced affine Lie algebras g. This is achieved by employing an embedding of the integrable highest weight modules of g into the Fock space for a bosonic string compactified on the weight lattice of g. Our vertex operators are universal in the sense that a single expression for the vertex operator holds simultaneously for all positive integral values of the level of g.