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Supersymmetry on Curved Spaces and Holography

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arxiv 1205.1062 v2 pith:RHRHG57J submitted 2012-05-04 hep-th

Claudius Klare , Alessandro Tomasiello , Alberto Zaffaroni This is my paper · ORCID
classification hep-th
keywords supersymmetriccomplexexistenceimpliesr-symmetryspacessuperconformalsupersymmetry
verification ladder T0 review T1 audit T2 compute T3 formal
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We study superconformal and supersymmetric theories on Euclidean four- and three-manifolds with a view toward holographic applications. Preserved supersymmetry for asymptotically locally AdS solutions implies the existence of a (charged) "conformal Killing spinor" on the boundary. We study the geometry behind the existence of such spinors. We show in particular that, in dimension four, they exist on any complex manifold. This implies that a superconformal theory has at least one supercharge on any such space, if we allow for a background field (in general complex) for the R-symmetry. We also show that this is actually true for any supersymmetric theory with an R-symmetry. We also analyze the three-dimensional case and provide examples of supersymmetric theories on Sasaki spaces.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 193 citations worldwide. 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. Topological Twisting of 4d $\mathcal{N}=2$ Supersymmetric Field Theories

    hep-th 2024-11 conditional novelty 8.0 of 10

    For any 4d N=2 theory, topologically twisted partition functions depend on the diffeomorphism type, 't Hooft fluxes, and a generalized spin-c structure.

  3. Chiralization of Quiver Varieties

    math.AG 2026-06 unverdicted novelty 6.0 of 10

    Constructs two vertex superalgebras chiralizing extended quiver varieties and establishes a map between them with vanishing and injectivity results under technical assumptions.

  4. Localizing AlAdS$_5$ black holes and the SUSY index on $S^1 \times M_3$

    hep-th 2025-11 conditional novelty 6.0 of 10

    The S^1×M_3 supersymmetric index for round, Lens, elliptically and biaxially squashed three-spheres is reproduced from D=5 equivariant localization after subtracting the Casimir energy via a gluing prescription.

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