Operator quantization of constrained WZNW theories and coset constructions

TL;DR

This paper develops an operator quantization framework for constrained WZNW theories and coset constructions, enabling the systematic inclusion of coset primary fields and currents within an associative algebra.

Contribution

It introduces a new algebraic construction for constrained WZNW models and coset theories using two Lie algebra-based WZNW theories, expanding the mathematical toolkit for these models.

Findings

Constructed an associative quotient algebra incorporating coset primary fields.

Provided a systematic method for operator quantization of constrained WZNW theories.

Extended the algebraic structure to include currents and primary fields in coset models.

Abstract

Using two WZNW theories for Lie algebras $g$ and $h, h\subset g,$ we construct the associative quotient algebra which includes a class of $g/h$ coset primary fields and currents.