AdS${}_3$ solutions in Massive IIA with small $\mathcal{N}=(4,0)$ supersymmetry

Abstract

We study AdS${}_3\times {\text{S}}^2$ solutions in massive IIA that preserve small $\mathcal{N}=(4,0)$ supersymmetry in terms of an SU(2)-structure on the remaining internal space. We find two new classes of solutions that are warped products of the form AdS${}_3\times {\text{S}}^2\times {\text{M}}_4\times \mathbb{R}$. For the first, M${}_4$=CY${}_2$ and we find a generalisation a D4-D8 system involving possible additional branes. For the second, M${}_4$ need only be Kahler, and we find a generalisation of the T-dual of solutions based on D3-branes wrapping curves in the base of an elliptically fibered Calabi-Yau 3-fold. Within these classes we find many new locally compact solutions that are foliations of AdS${}_3\times {\text{S}}^2\times {\text{CY}}_2$ over an interval, bounded by various D brane and O plane behaviours. We comment on how these local solutions may be used as the building blocks of infinite classes of global solutions glued together with defect branes. Utilising T-duality we find two new classes of AdS${}_3\times {\text{S}}^3\times {\text{M}}_4$ solutions in IIB. The first backreacts D5s and KK monopoles on the D1-D5 near horizon. The second is a generalisation of the solutions based on D3-branes wrapping curves in the base of an elliptically fibered CY${}_3$ that includes non trivial 3-form flux.

v3: 42 pages + appendices, typos corrected

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