Poisson-Lie Duality in the String Effective Action

TL;DR

This paper explores the symmetry properties of the bosonic string effective action under Poisson-Lie duality, presenting a simplified formulation and conditions for invariance, along with a relation between anomaly coefficients.

Contribution

It introduces a simple formulation of Poisson-Lie duality transformations and identifies conditions for the invariance of the string effective action.

Findings

The effective action remains invariant if the Drinfeld double's Lie algebras have traceless structure constants.

A functional relation between the Weyl anomaly coefficients of original and dual models is established.

The formulation simplifies the analysis of Poisson-Lie duality in string theory.

Abstract

The symmetry properties of the bosonic string effective action under Poisson-Lie duality transformations are investigated. A convenient and simple formulation of these duality transformations is found, that allows the reduction of the string effective action in a Kaluza-Klein framework. It is shown that the action is invariant provided that the two Lie algebras, forming the Drinfeld double, have traceless structure constants. Finally, a functional relation is found between the Weyl anomaly coefficients of the original and dual non-linear sigma models.