Branes wrapped on orbifolds and their gravitational blocks

Abstract

We construct new supersymmetric ${\mathrm{AdS}}_2\times {\mathbb{M}}_4$ solutions of $D=6$ gauged supergravity, where ${\mathbb{M}}_4$ are certain four-dimensional orbifolds. After uplifting to massive type IIA supergravity these correspond to the near-horizon limit of a system of $N$ D4-branes and $N_f$ D8-branes wrapped on ${\mathbb{M}}_4$. In one class of solutions ${\mathbb{M}}_4={\Sigma }_{\mathrm{g}}⋉\Sigma$ is a spindle fibred over a smooth Riemann surface of genus $\mathrm{g}>1$, while in another class ${\mathbb{M}}_4=\Sigma ⋉\Sigma$ is a spindle fibred over another spindle. Both classes can be thought of as orbifold generalizations of Hirzebruch surfaces and, in the second case, we describe the solutions in terms of toric geometry. We show that the entropy associated with these solutions is reproduced by extremizing an entropy function obtained by gluing gravitational blocks, using a general recipe for orbifolds that we propose. We also discuss how our prescription can be used to define an off-shell central charge whose extremization reproduces the gravitational central charge of analogous ${\mathrm{AdS}}_3\times {\mathbb{M}}_4$ solutions of $D=7$ gauged supergravity, arising from wrapping M5-branes on ${\mathbb{M}}_4$.

50 pages, 4 figures. v2: minor changes, references added. v3: minor changes, published version

References in corpus (23)

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• Accelerating Black Holes and Spinning Spindles
• D3-branes wrapped on a spindle
• Thermodynamics of accelerating and supersymmetric $Ad{S}_4$ black holes
• Supersymmetric spindles
• M5-branes wrapped on a spindle
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• D4-branes wrapped on a spindle
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• Resolutions of non-regular Ricci-flat Kahler cones
• D3-branes and M5-branes wrapped on a topological disc
• A tale of (M)2 twists
• Black holes with spindles at the horizon
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• Holographic duals of M5-branes on an irregularly punctured sphere
• Leigh-Strassler compactified on a spindle
• M2-branes wrapped on a topological disk
• Five-branes wrapped on topological disks from 7D N=2 gauged supergravity

Cited by in corpus (10)

• Equivariant localization and holography
• The Spindle Index from Localization
• Localizing Wrapped M5-branes and Gravitational Blocks
• $T^{1,1}$ truncation on the spindle
• NUTs, Bolts, and Spindles
• From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone)
• Branes wrapped on quadrilaterals
• New supersymmetric AdS${}_6$ black holes from matter-coupled F(4) gauged supergravity
• Supersymmetric localisation of $\mathcal{N}=(2,2)$ theories on a spindle
• Supersymmetric AdS${}_6$ black holes from ISO(3)xU(1) F(4) gauged supergravity