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

TL;DR

This paper derives conditions for N=1 supersymmetric flux vacua in massive Type IIA supergravity, characterizing internal geometries and flux configurations, and exploring implications with D6-branes for chiral gauge sectors.

Contribution

It provides explicit conditions for supersymmetric flux backgrounds with SU(3) and SU(2) structures in massive Type IIA supergravity, including examples with intersecting D6-branes.

Findings

SU(3)-structure implies nearly Kähler internal space with fluxes and negative cosmological constant.

Explicit example of conformally flat internal space with SU(2)-structure.

Framework for constructing chiral N=1 supersymmetric flux vacua with D-branes.

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 K\"ahler 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.