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

Abstract

In the first half of the paper, we study in details N S-branes, including the N S5-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 N S-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) × ℝ+ Dirac operator. Generalized Geometry allows us in addition to express the equations of motion explicitly in terms of fluxes. In the second half, we perform a general analysis of ten-dimensional geometric backgrounds with non-geometric fluxes, in the context of β-supergravity. We determine a well-defined class of such vacua, that are non-geometric in standard supergravity: they involve β-transforms, a manifest symmetry of β-supergravity with isometries. We show as well that these vacua belong to a geometric T-duality orbit. © 2014 The Author(s).