Domain Walls, Hitchin's Flow Equations and G_2-Manifolds

TL;DR

The paper analyzes BPS domain-wall solutions in four-dimensional gauged $ math N=2$ supergravity arising from Type-IIA compactifications on half-flat manifolds. It shows that the vector-multiplet flow equations are universal, while hypermultiplet flows depend on the specific gauging, and demonstrates that the domain-wall dynamics can be lifted to ten dimensions by identifying the flow with Hitchin's equations. This leads to a seven-manifold $Y_7$ with $G_2$ holonomy and a ten-dimensional background of the form $R^{1,2} imes Y_7$, confirming the consistency of the 4D action with the higher-dimensional equations of motion. The work explicitly constructs domain-wall solutions for a generalized axion gauging and establishes the precise matching to Hitchin flow data, thereby bridging 4D gauged supergravity, Hitchin's geometric flows, and $G_2$-holonomy geometry in string compactifications, with implications for mirror symmetry and possible uplifts to M-theory.

Abstract

We construct BPS domain wall solutions of the effective action of type-IIA string theory compactified on a half-flat six-manifold. The flow equations for the vector and hypermultiplet scalars are shown to be equivalent to Hitchin's flow equations, implying that our domain walls can be lifted to solutions of ten-dimensional type-IIA supergravity. They take the form R^{1,2} x Y_7, where Y_7 is a G_2-holonomy manifold with boundaries.