Fluxes of Courant bracket twisted at the same time by $B$ and $\theta$
Abstract
This paper investigates the simultaneous twisting of the Courant bracket by a 2-form and a bi-vector , exploring the generalized fluxes obtained in Courant algebroid relations. We define the twisted Lie bracket and demonstrate that the generalized -flux can be expressed as the field strength defined on this Lie algebroid. Similarly, we show that the -flux is a direct consequence of simultaneous twisting, which arises in the twisted Lie bracket relations between holonomic partial derivatives. We obtain the generalized flux in terms of the twisted Koszul bracket, which is a quasi-Lie algebroid bracket. The action of an exterior derivative related to the twisted Koszul bracket on a bi-vector produces the generalized -flux. We show that the generalized -flux is also the twisted Schouten-Nijenhuis bracket, i.e. the natural graded bracket on multi-vectors defined with the twisted Lie bracket.
Keywords
Cite
@article{arxiv.2312.11268,
title = {Fluxes of Courant bracket twisted at the same time by $B$ and $\theta$},
author = {Ljubica Davidović and Ilija Ivanišević and Branislav Sazdović},
journal= {arXiv preprint arXiv:2312.11268},
year = {2025}
}