N=1 domain wall solutions of massive type II supergravity as generalized geometries

TL;DR

The work addresses $N=1$ domain-wall solutions in type IIB string theory on Calabi-Yau manifolds with RR and NS flux, showing that transverse scalar dynamics obey a gradient flow driven by a single superpotential $W$. It derives explicit flow equations for vector and hypermultiplets and solves them, revealing a mirror Type IIA description as a generalized Hitchin flow on a manifold with $SU(3)\times SU(3)$ structure. This IIA picture corresponds to a seven-dimensional warped product $M^{1,2}\times_w X_7$ with an integrable $G_2\times G_2$ structure, linking flux-induced domain walls to geometric flows via pure spinors $\Phi_\pm$ and a matching superpotential $W$. Overall, the paper unifies flux-induced $N=1$ DW solutions with generalized geometry, providing a concrete bridge between IIB flux backgrounds and geometric compactifications in IIA.

Abstract

We study N=1 domain wall solutions of type IIB supergravity compactified on a Calabi-Yau manifold in the presence of RR and NS electric and magnetic fluxes. We show that the dynamics of the scalar fields along the direction transverse to the domain wall is described by gradient flow equations controlled by a superpotential W. We then provide a geometrical interpretation of the gradient flow equations in terms of the mirror symmetric compactification of type IIA. They correspond to a set of generalized Hitchin flow equations of a manifold with SU(3)xSU(3)structure which is fibered over the direction transverse to the domain wall.