Quantum Poisson-Lie T-duality and WZNW model

TL;DR

This paper constructs a pair of conformal sigma models connected by quantum Poisson-Lie T-duality, linking the SL(2,R) WZNW model to a constrained sigma model on the same group space, and proves their quantum equivalence.

Contribution

It introduces a new pair of conformal sigma models related by Poisson-Lie T-duality and demonstrates their quantum equivalence using path integral methods.

Findings

Established quantum equivalence of dual models

Linked WZNW model to constrained sigma model

Utilized O(2,2) Drinfeld double for construction

Abstract

A pair of conformal sigma models related by Poisson-Lie T-duality is constructed by starting with the O(2,2) Drinfeld double. The duality relates the standard SL(2,R) WZNW model to a constrained sigma model defined on SL(2,R) group space. The quantum equivalence of the models is established by using a path integral argument.