Mink${}_3\times S^3$ solutions of type II supergravity

Abstract

We initiate the classification of supersymmetric solutions of type II supergravity on ${\mathbb{R}}^{1,2}\times S^3\times M_4$. We find explicit local expressions for all backgrounds with either a single Killing spinor or two of equal norm, up to PDE's. We show that the only type II AdS${}_4\times S^3$ solution is the known $\mathcal{N}=4$ AdS${}_4$ background obtained from the near-horizon limit of intersecting D2-D6 branes. Various known branes and intersecting brane systems are recovered, and we obtain a novel class of ${\mathbb{R}}^{1,2}\times S^2\times S^3$ solutions in IIA.

v2: Typos corrected, section 3.2 expanded

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Cited by in corpus (8)

• AdS${}_3$ solutions in Massive IIA with small $\mathcal{N}=(4,0)$ supersymmetry
• AdS${}_3$ solutions with exceptional supersymmetry
• Type II Solutions on AdS${}_3\times S^3\times S^3$ with Large Superconformal Symmetry
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• AdS${}_3$ solutions with $\mathcal{N}=(3,0)$ from S${}^3\times$S${}^3$ fibrations
• The geometry of $\mathcal{N}=3$ AdS${}_4$ in massive IIA
• D-branes and non-Abelian T-duality
• Mink${}_4\times S^2$ Solutions of 10 and 11 Dimensional Supergravity