Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models

TL;DR

This paper constructs and analyzes 3D conformally invariant sigma models using Poisson-Lie T-plurality, providing explicit examples, dual models, and discussing quantum duality challenges.

Contribution

It introduces new 3D conformally invariant sigma models based on Drinfeld doubles and explores their T-plurality and dualities, including quantum obstacles.

Findings

Examples of conformally invariant models with vanishing beta-functions.

Dual models with nontrivial dilaton fields.

Identification of obstacles in quantum duality construction.

Abstract

Starting from the classification of 6-dimensional Drinfeld doubles and their decomposition into Manin triples we construct 3-dimensional Poisson-Lie T-dual or more precisely T-plural sigma models. Of special interest are those that are conformally invariant. Examples of models that satisfy vanishing beta-function equations with zero dilaton are presented and their duals are calculated. It turns out that for "traceless" dual algebras they satisfy the beta-function equations as well but usually with rather nontrivial dilaton. We also present explicit examples of several kinds of obstacles and difficulties present in construction of quantum dual models. Such concrete examples might be helpful in further development and improvement of quantum version of Poisson-Lie T-duality.