NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes

Understand

In the first half of the paper, we study in details NS-branes, including the NS5-brane, the Kaluza-Klein monopole and the exotic $5_2^2$- or Q-brane, together with Bianchi identities for NSNS (non)-geometric fluxes.

• Four-dimensional Bianchi identities are generalized to ten dimensions with non-constant fluxes, and get corrected by a source term in presence of an NS-brane.
• The latter allows them to reduce to the expected Poisson equation.
• Without sources, our Bianchi identities are also recovered by squaring a nilpotent $Spin(D,D) \times \mathbb{R}^+$ Dirac operator.