Flat coordinates and dilaton fields for three--dimensional conformal sigma models

TL;DR

This paper derives flat coordinates and dilaton fields for three-dimensional conformal sigma models, facilitating the analysis of their conformal invariance and duality properties.

Contribution

It provides explicit methods to find flat coordinates and dilaton fields for three-dimensional conformal sigma models using differential equations from connection transformations.

Findings

Explicit flat coordinates for the models are obtained.

General forms of dilaton fields satisfying beta function equations are derived.

The approach aids in understanding conformal invariance in sigma models.

Abstract

Riemannian coordinates for flat metrics corresponding to three--dimensional conformal Poisson--Lie T--dualizable sigma models are found by solving partial differential equations that follow from the transformations of the connection components. They are then used for finding general forms of the dilaton fields satisfying the vanishing beta equations of the sigma models.