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

TL;DR

This paper constructs BPS domain wall solutions in type-IIA string theory compactified on half-flat manifolds, showing their equivalence to Hitchin's flow equations and their lift to G_2-holonomy manifolds in ten dimensions.

Contribution

It establishes a link between domain wall solutions and Hitchin's flow equations, enabling lift to G_2-holonomy manifolds in ten-dimensional supergravity.

Findings

Domain walls correspond to G_2-holonomy manifolds with boundaries.

Flow equations for scalars match Hitchin's flow equations.

Solutions can be lifted to ten-dimensional supergravity.

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.