Supersymmetric Intersecting D6-branes and Fluxes in Massive Type IIA String Theory

TL;DR

This work constructs 4D $N=1$ vacua in massive Type IIA string theory with intersecting D6-branes and NS-NS flux, deriving explicit supersymmetry conditions and the SU(3)-to-SU(2) structure transition induced by fluxes. The analysis shows that the mass parameter $m$ enforces a vector $v$ and an $SU(2)$-structure, with $dF=mH$ and $F woheadrightarrow$ constraints that relate fluxes to warping and intrinsic torsion, including a D8-brane interpretation for $m eq0$. Anomaly inflow calculations indicate the D6 world-volume gauge theory remains non-chiral under these configurations, and moduli dynamics are constrained by the flux setup, yielding a limited but structured moduli stabilization. The paper discusses singular warp factors, potential regularizations via harmonic fluxes, and future extensions, notably including RR 4-form flux to realize chirality and connect to M-theory on manifolds with G2 structure.

Abstract

We study N=1 supersymmetric four-dimensional solutions of massive Type IIA supergravity with intersecting D6-branes in the presence NS-NS three-form fluxes. We derive N=1 supersymmetry conditions for the D6-brane and flux configurations in an internal manifold $X_6$ and derive the intrinsic torsion (or SU(3)-structure) related to the fluxes. In the absence of fluxes, N=1 supersymmetry implies that D6-branes wrap supersymmetric three-cycles of $X_6$ that intersect at angles of SU(3) rotations and the geometry is deformed by SU(3)-structures. The presence of fluxes breaks the SU(3) structures to SU(2) and the D6-branes intersect at angles of SU(2) rotations; non-zero mass parameter corresponds to D8-branes which are orthogonal to the common cycle of all D6-branes. The anomaly inflow indicates that the gauge theory on intersecting (massive) D6-branes is not chiral.