# Effective Actions for $\sigma$-Models of Poisson-Lie Type

## TL;DR

This paper develops a generalized geometric framework for understanding Poisson-Lie T-duality in string theory, incorporating Courant algebroids and a Levi-Civita connection to describe effective actions.

## Contribution

It introduces a novel approach using Courant algebroids and generalized geometry to formulate string effective actions for Poisson-Lie sigma models, including a new way to encode the dilaton.

## Key findings

- Explicit background solutions are constructed.
- A generalized Levi-Civita connection is formulated.
- The framework unifies T-duality and geometric structures.

## Abstract

(Quasi-)Poisson-Lie T-duality of string effective actions is described in the framework of generalized geometry of Courant algebroids. The approach is based on a generalization of Riemannian geometry in the context of Courant algebroids, including a proper version of a Levi-Civita connection. In our approach, the dilaton field is encoded in a Levi-Civita connection and its form is determined by the Courant algebroid geometry. Explicit examples of background solutions are provided using the approach developed in the paper.