Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models II: Nondiagonal metrics and dilaton puzzle

TL;DR

This paper investigates three-dimensional Poisson-Lie dualizable sigma models with constant dilaton fields, exploring their properties under T-plurality, and addresses the dilaton puzzle in dual models with nontrivial dilaton fields.

Contribution

It extends the understanding of Poisson-Lie T-plurality to models with nontrivial dilaton fields and provides criteria for when the dilaton cannot be consistently defined in dual models.

Findings

Models with traceless dual algebras satisfy beta-function equations.

In some dual models, the dilaton cannot be defined, explained by specific criteria.

Constructed models correspond to various decompositions of Drinfeld doubles.

Abstract

We look for 3-dimensional Poisson-Lie dualizable sigma models that satisfy the vanishing beta-function equations with constant dilaton field. Using the Poisson-Lie T-plurality we then construct 3-dimensional sigma models that correspond to various decompositions of Drinfeld double. Models with nontrivial dilaton field may appear. It turns out that for ``traceless'' dual algebras they satisfy the vanishing beta-function equations as well. In certain cases the dilaton cannot be defined in some of the dual models. We provide an explanation why this happens and give criteria predicting when it happens.