Fibred GK geometry and supersymmetric $AdS$ solutions

Abstract

We continue our study of a general class of $\mathcal{N}=2$ supersymmetric $Ad{S}_3\times Y_7$ and $Ad{S}_2\times Y_9$ solutions of type IIB and $D=11$ supergravity, respectively. The geometry of the internal spaces is part of a general family of "GK geometries", $Y_{2n+1}$, $n\ge 3$, and here we study examples in which $Y_{2n+1}$ fibres over a Kähler base manifold $B_{2k}$, with toric fibres. We show that the flux quantization conditions, and an action function that determines the supersymmetric $R$-symmetry Killing vector of a geometry, may all be written in terms of the "master volume" of the fibre, together with certain global data associated with the Kähler base. In particular, this allows one to compute the central charge and entropy of the holographically dual $(0,2)$ SCFT and dual superconformal quantum mechanics, respectively, without knowing the explicit form of the $Y_7$ or $Y_9$ geometry. We illustrate with a number of examples, finding agreement with explicit supergravity solutions in cases where these are known, and we also obtain new results. In addition we present, en passant, new formulae for calculating the volumes of Sasaki-Einstein manifolds.

arXiv comment49 pages

References in corpus (22)

• Black hole microstates in AdS${}_4$ from supersymmetric localization
• Sasaki-Einstein Manifolds and Volume Minimisation
• The Geometric Dual of a-maximisation for Toric Sasaki-Einstein Manifolds
• Exact two-dimensional superconformal R-symmetry and c-extremization
• Exact microstate counting for dyonic black holes in AdS4
• AdS(3) Solutions of IIB Supergravity from D3-branes
• A Universal Counting of Black Hole Microstates in AdS${}_4$
• Supersymmetric AdS_3, AdS_2 and Bubble Solutions
• Notes on toric Sasaki-Einstein seven-manifolds and AdS_4/CFT_3
• Holographic microstate counting for AdS${}_4$ black holes in massive IIA supergravity
• AdS spacetimes from wrapped M5 branes
• Black hole entropy in massive Type IIA
• Supersymmetric AdS_3 solutions of type IIB supergravity
• Comments on AdS2 solutions of D=11 Supergravity
• Microstate Counting of $Ad{S}_4$ Hyperbolic Black Hole Entropy via the Topologically Twisted Index
• A geometric dual of $c$-extremization
• Geometries with Killing Spinors and Supersymmetric AdS Solutions
• Geometry of $\mathcal{I}$-extremization and black holes microstates
• Toric geometry and the dual of $c$-extremization
• Proving the equivalence of $c$-extremization and its gravitational dual for all toric quivers
• Supersymmetric wrapped membranes, AdS(2) spaces, and bubbling geometries
• AdS spacetimes from wrapped D3-branes

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• D4-branes wrapped on a spindle
• Equivariant localization and holography
• Localization and Attraction
• Universal AdS black holes in theories with sixteen supercharges and their microstates
• Twisted $\mathcal{N}=1$ SCFTs and their AdS${}_3$ duals
• On Type IIA AdS${}_3$ solutions and massive GK geometries
• $\mathcal{I}$/$c$-Extremization in M/F-Duality
• The Near-Horizon Geometry of Supersymmetric Rotating AdS${}_4$ Black Holes in M-theory
• Superconformal Quantum Mechanics on Kähler Cones
• $N=(2,0)$ AdS${}_3$ Solutions of M-theory
• Uplifting dyonic AdS${}_4$ black holes on seven-dimensional Sasaki-Einstein manifolds
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