General N = 1 Supersymmetric Fluxes in Massive Type IIA String Theory

TL;DR

This work derives the supersymmetry conditions for general fluxes in massive Type IIA string theory, focusing on SU(3) and SU(2) internal structures. It shows that SU(3) fluxes with nonzero mass force the internal space to be nearly Kähler, with all fluxes tied to the mass and the dilaton fixed by flux ratios, yielding a negative cosmological constant and an AdS$_4$ vacuum. In contrast, SU(2) structures admit a Minkowski external space with a conformally flat internal geometry, and there exists an explicit, fully determined flux vacuum that accommodates intersecting D6-branes and calculable chiral spectra. The results provide a concrete basis for constructing four-dimensional, chiral ${\cal N}=1$ flux vacua in massive IIA with D-branes, and they illuminate moduli stabilization and cosmological constant considerations within these frameworks.

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 Kähler 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.