AdS$_3$ solutions with $\mathcal{N}=(3,0)$ from S$^3\times$S$^3$ fibrations

We study warped AdS$_3$ solutions in massive IIA supergravity preserving $\mathcal{N}=(3,0)$ and $\mathcal{N}=(1,0)$ supersymmetry. We consider solutions whose internal spaces decompose as an S$^3\times$S$^3$ fibration and a interval over which the rest of the solution is foliated. We present necessary and sufficient conditions for these solutions to exist, in terms of systems of ordinary differential equations and find several new analytic and numerical examples with internal spaces bounded between D-brane and O-plane behaviors.

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