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Gravitational Blocks, Spindles and GK Geometry

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arxiv 2211.02662 v2 pith:5VKPMGHI submitted 2022-11-04 hep-th

Andrea Boido , Jerome P. Gauntlett , Dario Martelli , James Sparks This is my paper · ORCID
classification hep-th
keywords solutionssupersymmetricgravitationalactionblockgeneralsupergravityformula
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We derive a gravitational block formula for the supersymmetric action for a general class of supersymmetric AdS solutions, described by GK geometry. Extremal points of this action describe supersymmetric AdS$_3$ solutions of type IIB supergravity, sourced by D3-branes, and supersymmetric AdS$_2$ solutions of $D=11$ supergravity, sourced by M2-branes. In both cases, the branes are also wrapped over a two-dimensional orbifold known as a spindle, or a two-sphere. We develop various geometric methods for computing the gravitational block contributions, allowing us to recover previously known results for various explicit supergravity solutions, and to significantly generalize these results to other compactifications. For the AdS$_3$ solutions we give a general proof that our off-shell supersymmetric action agrees with an appropriate off-shell $c$-function in the dual field theory, establishing a very general exact result in holography. For the AdS$_2$ solutions our gravitational block formula allows us to obtain the entropy for supersymmetric, magnetically charged and accelerating black holes in AdS$_4$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Supersymmetric $\mathbb{WCP}^n$, AdS near horizons and orbifolds

    hep-th 2025-11 conditional novelty 7.0 of 10

    Weighted projective spaces WCP² and WCP³ can be made supersymmetric for tuned integer weights, yielding new AdS₅×WCP²×S¹, AdS₄×WCP³, and AdS₃×WT(1,1) supergravity solutions.

  2. NUTs, Bolts, and Spindles

    hep-th 2024-11 conditional novelty 7.0 of 10

    New infinite families of supersymmetric spindle-bolt solutions with branched lens-space boundaries are constructed, with on-shell actions matching equivariant localization.

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