Bianchi Identities for Non-Geometric Fluxes - From Quasi-Poisson Structures to Courant Algebroids

TL;DR

This paper derives generalized Bianchi identities for non-geometric fluxes using quasi-Poisson structures and connects these results to Courant algebroids, advancing the mathematical framework of string theory flux compactifications.

Contribution

It introduces a novel derivation of Bianchi identities from quasi-Poisson structures and relates them to Courant algebroids, providing a new mathematical perspective.

Findings

Derived the most general Bianchi identities for fluxes H,f,Q,R.

Connected quasi-Poisson structures to Courant algebroids.

Established a mathematical framework linking non-geometric fluxes to algebroid structures.

Abstract

Starting from a (non-associative) quasi-Poisson structure, the derivation of a Roytenberg-type algebra is presented. From the Jacobi identities of the latter, the most general form of Bianchi identities for fluxes (H,f,Q,R) is then derived. It is also explained how this approach is related to the mathematical theory of quasi-Lie and Courant algebroids.