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Localization of the free energy in supergravity

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arxiv 2407.02554 v3 pith:62FUTQTN submitted 2024-07-02 hep-th

classification hep-th
keywords supergravityenergyfreeresultssolutionsallowsassumingcomputations
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We derive a general formula for the gravitational free energy of Euclidean supersymmetric solutions to $D=4$, $\mathcal{N}=2$ gauged supergravity coupled to vector multiplet matter. This allows one to compute the free energy without solving any supergravity equations, just assuming the solutions exist. As well as recovering some known results in the literature with ease, we also present new supergravity results that match with holographically dual field theory computations.

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Cited by 3 Pith papers

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

  1. Ten-dimensional localization

    hep-th 2026-07 conditional novelty 7.0 of 10

    Equivariantly closed polyforms for type II Page fluxes and actions enable direct 10D localization of on-shell actions and flux quantization for minimally supersymmetric backgrounds.

  2. $\mathcal{N}=2$ Super Yang-Mills in AdS$_4$ and $F_{\text{AdS}}$-maximization

    hep-th 2025-06 conditional novelty 7.0 of 10

    A new maximization principle, F_AdS-maximization, selects boundary conditions for N=2 SYM in AdS4 and predicts a transition to a U(1)-Higgsed phase at strong coupling.

  3. 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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