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Localization of the action in AdS/CFT

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arxiv 1906.11249 v1 pith:TIVPTP7E submitted 2019-06-26 hep-th

Pietro Benetti Genolini , Juan Manuel Pérez Ipiña , James Sparks This is my paper · ORCID
classification hep-th
keywords actionformulasupersymmetricfieldsimplesolutionsolutionstopological
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We derive a simple formula for the action of any supersymmetric solution to minimal gauged supergravity in the AdS$_4$/CFT$_3$ correspondence. Such solutions are equipped with a supersymmetric Killing vector, and we show that the holographically renormalized action may be expressed entirely in terms of the weights of this vector field at its fixed points, together with certain topological data. In this sense, the classical gravitational partition function localizes in the bulk. We illustrate our general formula with a number of explicit examples, in which exact dual field theory computations are also available, which include supersymmetric Taub-NUT and Taub-bolt type spacetimes, as well as black hole solutions. Our simple topological formula also allows us to write down the action of any solution, provided it exists.

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Cited by 4 Pith papers

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

  1. Equivariant localization for $D=4$ gauged supergravity

    hep-th 2024-12 conditional novelty 8.0 of 10

    Supersymmetric Euclidean D=4 N=2 gauged supergravity actions and fluxes localize onto R-symmetry fixed points, proving large-N SCFT free-energy formulas and UV-IR relations.

  2. Mixed 't Hooft Anomalies and the Witten Effect for AdS Black Holes

    hep-th 2024-12 conditional novelty 7.0 of 10

    Near-BPS dyonic AdS4 black holes with a theta angle show a Witten-effect charge shift that reduces the mass gap and the index, and at the special angle both the Bekenstein-Hawking entropy and the supersymmetric index ...

  3. 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.

  4. Ensembles in M-theory and Holography

    hep-th 2025-05 conditional novelty 6.0 of 10

    The M2-brane partition function should be viewed as a grand canonical object in AdS4/ABJM holography, fixing the three-form source rather than the flux number N, which resolves puzzles about Airy shifts and one-loop e...

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