Courant Algebroid Relations, T-Dualities and Generalised Ricci Flow

TL;DR

This paper develops a framework linking Courant algebroid relations, T-duality, and generalised Ricci flow, demonstrating that T-duality preserves solutions of the flow and providing explicit examples.

Contribution

It introduces a novel notion of Courant algebroid relations and invariant divergences, establishing T-duality as compatible with generalised Ricci flow and string background equations.

Findings

T-duality relates divergence operators on Courant algebroids.

T-duality preserves solutions of generalised Ricci flow.

Explicit examples illustrate the theoretical constructions.

Abstract

The notion of Courant algebroid relation is used to introduce a definition of relation between divergence operators on Courant algebroids. By introducing invariant divergence operators, a notion of generalised T-duality between divergences is presented through an existence and uniqueness result for related divergence operators on T-dual pairs of exact Courant algebroids, which naturally incorporates the dilaton shift. When combined with the notion of generalised isometry, this establishes circumstances under which generalised Ricci tensors are related, proving that T-duality is compatible with generalised string background equations. This enables an analysis of the compatibility between T-duality and generalised Ricci flow, showing that the T-dual of a solution of generalised Ricci flow is also a solution of generalised Ricci flow. Our constructions are illustrated through many explicit examples.