Courant algebroid without constraints on fluxes on its Dirac structures

TL;DR

This paper investigates the structure of Courant algebroids and Dirac structures in string theory, demonstrating that certain twisted algebroids can have unrestricted fluxes, expanding understanding of their geometric properties.

Contribution

It shows that Courant algebroids twisted by both B-fields and theta parameters can have Dirac structures with no flux restrictions, revealing new flexibility in their geometric framework.

Findings

Courant algebroids twisted by B and theta have unrestricted fluxes.

Dirac structures impose constraints on fluxes in standard cases.

The combined twist leads to flux freedom in Dirac structures.

Abstract

We examine the standard Courant bracket and its extensions, defined by twists with different $O(D,D)$ transformations relevant to string theory. We analyze Dirac structures on these Courant algebroids and derive the constraints they impose on fluxes. In the end, we show that the Courant algebroid simultaneously twisted by both $B$ and $\theta$ is characterized by Dirac structures with no restrictions on fluxes.