Courant algebroids, Poisson-Lie T-duality, and type II supergravities

TL;DR

This paper develops a generalized geometric framework for Courant algebroids to analyze Poisson-Lie T-duality and supergravity solutions, extending previous results to broader classes of dualities and backgrounds.

Contribution

It reformulates Ricci curvature notions on Courant algebroids, proves compatibility of Poisson-Lie T-duality with RG flow and supergravity equations, and introduces new solutions on symmetric spaces.

Findings

Compatibility of Poisson-Lie T-duality with renormalization group flow.

Extension of duality results to gauged cases like dressing cosets.

New supergravity solutions on symmetric spaces.

Abstract

We reexamine the notions of generalized Ricci tensor and scalar curvature on a general Courant algebroid, reformulate them using objects natural w.r.t. pull-backs and reductions, and obtain them from the variation of a natural action functional. This allows us to prove, in a very general setup, the compatibility of the Poisson-Lie T-duality with the renormalization group flow and with string background equations. We thus extend the known results to a much wider class of dualities, including the cases with gauging (so called dressing cosets, or equivariant Poisson-Lie T-duality). As an illustration, we use the formalism to provide new classes of solutions of modified supergravity equations on symmetric spaces.