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1/4 BPS solutions in massive IIA supergravity
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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.
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Wrapped Brane Solutions in Romans $F(4)$ Gauged Supergravity
Wrapped D4-branes in Romans F(4) gauged supergravity are mapped to supersymmetric and non-supersymmetric AdS vacua, with new non-BPS AdS2 solutions whose stability is checked against the Breitenlohner-Freedman bound.
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