1/4 BPS solutions in massive IIA supergravity

TL;DR

This work constructs four 1/4 BPS configurations in massive IIA supergravity that include D8-branes as domain walls separating regions with differing mass parameter $m$. By enforcing supersymmetry, the authors derive master equations in terms of two functions $S(z,r)$ and $K(z,r)$ (or equivalent harmonic functions) that encode D6-NS5, D8-D0-F1, D8-D2, and D8-D4 systems; some solutions are governed by nonlinear PDEs, while others admit harmonic-function representations. The paper provides explicit massless and massive examples, develops domain-wall matching and BPS boundary conditions, and presents curved D8-brane and BIon-type configurations, illustrating a rich set of interfaces between massive regions and their brane content. These results offer a framework for analyzing low-dimensional gauge theories via brane probes in massive backgrounds and highlight how charge correlations in Romans massive IIA constrain the solution space.

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.