General N=1 supersymmetric fluxes in massive type IIA string theory

Abstract We study conditions on general fluxes of massive type IIA supergravity that lead to four-dimensional backgrounds with N = 1 supersymmetry. We derive these conditions in the case of SU ( 3 ) - as well as SU ( 2 ) -structures. SU ( 3 ) -structures imply that the internal space is constrained to be a nearly Kahler manifold with all the turned on fluxes, and the negative cosmological constant proportional to the mass parameter, and the dilaton fixed by the quantized ratio of the three-form and four-form fluxes. We further discuss the implications of such flux vacua with added intersecting D6-branes, leading to the chiral non-Abelian gauge sectors (without orientifold projections). Examples that break SU ( 3 ) -structures to SU ( 2 ) -ones allow for the internal space conformally flat (up to orbifold and orientifold projections), for which we give an explicit example. These results provide a starting point for further study of the four-dimensional (chiral) N = 1 supersymmetric solutions of massive type IIA supergravity with D-branes and fluxes, compactified on orientifolds.