Minkowski${}_4$ $\times$ $S^2$ solutions of IIB supergravity

Abstract

We classify $\mathcal{N}=2$ Minkowski${}_4$ solutions of IIB supergravity with an $SU(2{)}_R$ symmetry geometrically realized by an $S^2$-foliation in the remaining six dimensions. For the various cases of the classification, we reduce the supersymmetric system of equations to PDEs. These cases often accommodate systems of intersecting branes and half-maximally supersymmetric AdS${}_{5,6,7}$ solutions when they exist. As an example, we analyze the AdS${}_6$ case in more detail, reducing the supersymmetry equations to a single cylindrical Laplace equation. We also recover an already known linear dilaton background dual to the $(1,1)$ Little String Theory (LST) living on NS5-branes, and we find a new Minkowski${}_5$ linear dilaton solution from brane intersections. Finally, we also discuss some simple Minkowski${}_4$ solutions based on compact conformal Calabi-Yau manifolds.

43 pages, 1 appendix. v2: typos corrected, references added

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• $Ad{S}_6$ T-duals and Type IIB $Ad{S}_6\times S^2$ Geometries with 7-Branes
• Black hole microstate counting in Type IIB from 5d SCFTs
• All $\mathcal{N}=(8,0)$ AdS${}_3$ solutions in 10 and 11 dimensions
• Electrostatic description of 3d $\mathcal{N}=4$ linear quivers
• Charting the landscape of (anti-) de Sitter and Minkowski solutions of 10d supergravities
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• Gravitational waves in warped compactifications
• Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d
• Massive flows in AdS${}_6$/CFT${}_5$
• The geometry of $\mathcal{N}=3$ AdS${}_4$ in massive IIA
• Breaking supersymmetry with pure spinors
• Non-integrability for $\mathcal{N}=1$ SCFTs in $5d$
• Mink${}_4\times S^2$ Solutions of 10 and 11 Dimensional Supergravity
• Uplifting supersymmetric $Ad{S}_6$ black holes to type II supergravity
• Holographic duals of $\mathcal{N}=1$ quivers in 5d and their nonrelativistic limits