1/4 BPS solutions in massive IIA supergravity

TL;DR

This paper investigates four types of 1/4 BPS solutions in massive IIA supergravity, revealing their structures and boundary conditions, with a focus on D8-D6-NS5 systems and the role of domain walls.

Contribution

It provides a unified approach to deriving these solutions from supersymmetry conditions, including novel treatment of D8-branes as domain walls connecting different mass parameters.

Findings

D8-D2 and D8-D4 solutions are harmonic functions.

D8-D6-NS5 solutions involve non-linear differential equations.

D8-branes can be modeled as domain walls with specific boundary conditions.

Abstract

We study four kinds of 1/4 BPS solutions in massive IIA supergravity corresponding to D8-D0-F1, D8-D2, D8-D4 and D8-D6-NS5 systems. We show that these solutions are reproduced without making nontrivial assumptions by using supersymmetry conditions. D8-D2 and D8-D4 solutions are represented by harmonic functions, as usual, while the other two are represented by solutions of non-linear differential equations. Because these four solutions can be treated in almost identical ways, we mainly focus on the D8-D6-NS5 systems. We first discuss D6-NS5 solutions with uniform mass parameters. Then, we introduce D8-branes as domain walls by connecting two solutions with different values of the mass parameter. We also discuss boundary conditions and supersymmetry on domain walls.