Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle

TL;DR

This paper introduces a new geometric method using Levi-Civita connections on Courant algebroids to address the dilaton puzzle in Poisson-Lie T-duality of string effective actions, establishing a duality framework at the effective action level.

Contribution

It presents a novel geometric approach to derive Poisson-Lie T-dual dilaton fields, extending T-duality to string effective actions with a new mathematical framework.

Findings

Formulas for Poisson-Lie T-dual dilaton fields derived.

Established a version of T-duality at the level of string effective actions.

Provided geometrical tools for analyzing dualities in string theory.

Abstract

For a particular class of backgrounds, equations of motion for string sigma models targeted in mutually dual Poisson-Lie groups are equivalent. This phenomenon is called the Poisson-Lie T-duality. On the level of the corresponding string effective actions, the situation becomes more complicated due to the presence of the dilaton field. A novel approach to this problem using Levi-Civita connections on Courant algebroids is presented. After the introduction of necessary geometrical tools, formulas for the Poisson-Lie T-dual dilaton fields are derived. This provides a version of Poisson-Lie T-duality for string effective actions.