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arxiv: 2508.08207 · v2 · submitted 2025-08-11 · ✦ hep-th

Equivariant localization for D=5 gauged supergravity

Pietro Benetti Genolini , Jerome P. Gauntlett , Yusheng Jiao , Jaeha Park , James Sparks This is my paper

Pith reviewed 2026-05-18 23:20 UTC · model grok-4.3

classification ✦ hep-th
keywords gauged supergravityequivariant localizationsupersymmetric solutionsdimensional reductionon-shell actionCasimir energysupersymmetric indexSCFT holography
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The pith

An extra Killing vector reduces D=5 gauged supergravity to four dimensions where equivariant localization evaluates the on-shell action.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out a procedure for evaluating the on-shell action of supersymmetric solutions in five-dimensional Euclidean gauged supergravity coupled to any number of vector multiplets. The solutions are required to possess both the R-symmetry Killing vector built from the Killing spinor and a second Killing vector. The second vector is used to reduce the five-dimensional theory to four-dimensional N=2 gauged supergravity, after which equivariant localization supplies the value of the original five-dimensional action. The method is applied to concrete cases to obtain the supersymmetric Casimir energy and the supersymmetric index of the dual superconformal field theory without constructing the explicit five-dimensional metric or fields.

Core claim

Supersymmetric solutions of D=5 Euclidean gauged supergravity that admit both the R-symmetry Killing vector K and an additional Killing vector ℓ can be dimensionally reduced along ℓ to D=4, N=2 gauged supergravity; the five-dimensional on-shell action is then obtained by equivariant localization on the reduced theory. The procedure yields the supersymmetric Casimir energy and the supersymmetric index of the dual SCFT directly from the reduced data, without reference to explicit five-dimensional solutions.

What carries the argument

The additional Killing vector ℓ, which generates the dimensional reduction from D=5 to D=4 N=2 gauged supergravity and thereby places the on-shell action in a form where equivariant localization applies.

If this is right

  • The supersymmetric Casimir energy is obtained from localization data in the reduced four-dimensional theory.
  • The supersymmetric index of the dual SCFT follows from the same localized computation.
  • The result holds for an arbitrary number of vector multiplets in the original five-dimensional theory.
  • Explicit construction of the five-dimensional fields is unnecessary once the reduced four-dimensional data are known.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same reduction-plus-localization route may apply to other dimensions or to supergravities with different matter content whenever a suitable extra Killing vector exists.
  • Direct comparison of the localized value with independent field-theory computations of the index could test the holographic dictionary at the level of the on-shell action.
  • The method suggests a systematic way to organize higher-derivative corrections once they are included in the five-dimensional action before reduction.

Load-bearing premise

The five-dimensional solutions must admit an extra Killing vector ℓ, in addition to the R-symmetry vector, that permits a consistent dimensional reduction to four dimensions.

What would settle it

An explicit five-dimensional solution whose on-shell action, computed by direct integration, differs from the value obtained by reducing along ℓ and applying localization would show the procedure does not hold.

read the original abstract

We consider supersymmetric solutions of $D=5$ Euclidean gauged supergravity coupled to an arbitrary number of vector multiplets. We consider solutions that admit both the R-symmetry Killing vector, $\mathcal{K}$, constructed as a bilinear in the Killing spinor, as well as an additional Killing vector $\ell$. Using $\ell$ to perform a dimensional reduction to $D=4$, $\mathcal{N}=2$ gauged supergravity, we show how the $D=5$ on-shell action can be computed using equivariant localization. We illustrate the formalism with some examples, computing the supersymmetric Casimir energy and the supersymmetric index of the dual SCFT without using the explicit supergravity solutions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper considers supersymmetric solutions of D=5 Euclidean gauged supergravity coupled to vector multiplets that admit both the R-symmetry Killing vector K (built from the Killing spinor) and an additional Killing vector ℓ. It performs a dimensional reduction along ℓ to obtain a D=4, N=2 gauged supergravity theory and then applies equivariant localization to compute the D=5 on-shell action. The formalism is illustrated with examples that extract the supersymmetric Casimir energy and the supersymmetric index of the dual SCFT without constructing explicit supergravity solutions.

Significance. If the reduction step maps the on-shell action exactly onto the 4D theory to which localization applies, the result supplies a practical route to 5D on-shell quantities (including boundary contributions relevant to holography) that bypasses explicit solution of the equations of motion. The approach extends existing localization techniques from 4D to 5D via a controlled reduction and directly yields quantities of interest for the dual SCFT, such as the index and Casimir energy.

major comments (1)
  1. [Dimensional reduction and on-shell action mapping] The central claim rests on the assertion that dimensional reduction along ℓ yields a D=4 theory whose on-shell action (including any topological or boundary terms) is identical to the original 5D action, so that equivariant localization on the reduced theory reproduces the 5D value. The abstract and the stated weakest assumption only guarantee the existence of ℓ and K; they do not address whether the reduction introduces a non-trivial warp factor, modifies the gauging parameters, or generates extra finite contributions that survive localization. A concrete check that the reduced equations of motion and the value of the action functional coincide with those of the standard 4D N=2 theory used in prior localization work is required.
minor comments (2)
  1. Clarify the precise relation between the 5D Killing spinor bilinear K and the 4D R-symmetry vector after reduction; the notation for the reduced fields and the gauging parameters should be stated explicitly.
  2. In the examples, specify which 4D localization formula is being invoked and confirm that the fixed-point data are insensitive to any residual warp-factor dependence.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive major comment. We address the point regarding the dimensional reduction and on-shell action mapping below.

read point-by-point responses

  1. Referee: [Dimensional reduction and on-shell action mapping] The central claim rests on the assertion that dimensional reduction along ℓ yields a D=4 theory whose on-shell action (including any topological or boundary terms) is identical to the original 5D action, so that equivariant localization on the reduced theory reproduces the 5D value. The abstract and the stated weakest assumption only guarantee the existence of ℓ and K; they do not address whether the reduction introduces a non-trivial warp factor, modifies the gauging parameters, or generates extra finite contributions that survive localization. A concrete check that the reduced equations of motion and the value of the action functional coincide with those of the standard 4D N=2 theory used in prior localization work is required.

    Authors: We thank the referee for this important observation. In the construction, the additional Killing vector ℓ is taken to be hypersurface-orthogonal with constant norm, allowing a Kaluza-Klein reduction with the metric ansatz ds_5² = ds_4² + (dy + A)^2 where the 4D fields are independent of the circle coordinate y. Under this reduction the 5D Euclidean gauged supergravity action (including the topological and boundary terms relevant for holography) integrates to the standard 4D N=2 gauged supergravity action used in the localization literature, with the gauging parameters and vector-multiplet data mapped in a one-to-one fashion. Because the original 5D configuration is on-shell, the reduced 4D fields automatically satisfy the 4D equations of motion; no additional finite contributions survive after the y-integration. We acknowledge that the current text does not contain an explicit appendix verifying every step of the reduction. We will therefore add a dedicated subsection (or short appendix) that performs this concrete check, confirming that the on-shell value of the action is preserved and that the reduced theory coincides with the one to which equivariant localization has previously been applied. revision: yes

Circularity Check

0 steps flagged

Derivation is self-contained; no circular reductions identified

full rationale

The paper derives the D=5 on-shell action by reducing along the additional Killing vector ℓ to D=4 N=2 gauged supergravity and then applying equivariant localization. This relies on the stated existence of K and ℓ (from the Killing spinor) and invokes a standard localization method on the reduced theory. No quoted step equates a claimed prediction or result to a fitted parameter, self-defined quantity, or load-bearing self-citation chain. The examples computing Casimir energy and index are presented as direct outputs of the method without reducing to the paper's own inputs by construction. The central claim remains independent of any circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions of supersymmetric supergravity; no free parameters, new entities, or ad-hoc axioms are introduced in the abstract description.

axioms (2)
  • domain assumption Existence of Killing spinors yielding an R-symmetry Killing vector K
    Standard assumption for supersymmetric solutions in gauged supergravity.
  • domain assumption Existence of an additional Killing vector ℓ permitting consistent dimensional reduction to D=4 N=2 gauged supergravity
    Required for the reduction step described in the abstract.

pith-pipeline@v0.9.0 · 5659 in / 1342 out tokens · 55313 ms · 2026-05-18T23:20:11.374723+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

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

  1. Probing black holes with equivariant localization

    hep-th 2026-04 unverdicted novelty 7.0

    Equivariant localization computes probe D3-brane actions in uplifted Kerr-Newman-AdS5 supergravity backgrounds, reducing them to toric-data integrals for SCFT indices.

  2. The superconformal index and localizing higher derivative supergravity

    hep-th 2026-04 unverdicted novelty 6.0

    Equivariant localization computes the on-shell action of D=5 AdS rotating charged black holes in higher-derivative supergravity, exactly matching the dual superconformal index in the Cardy limit.

Reference graph

Works this paper leans on

59 extracted references · 59 canonical work pages · cited by 2 Pith papers · 29 internal anchors

  1. [1]

    Classes caract´ eristiques ´ equivariantes. Formules de localisation en cohomologie ´ equivariante,

    N. Berline and M. Vergne, “Classes caract´ eristiques ´ equivariantes. Formules de localisation en cohomologie ´ equivariante,”C.R. Acad. Sc. Paris 295 (1982) 539–541

    work page 1982

  2. [2]

    The Moment map and equivariant cohomology,

    M. F. Atiyah and R. Bott, “The Moment map and equivariant cohomology,” Topology23 (1984) 1–28

    work page 1984

  3. [3]

    Equivariant Localization in Supergravity,

    P. Benetti Genolini, J. P. Gauntlett, and J. Sparks, “Equivariant Localization in Supergravity,” Phys. Rev. Lett. 131 no. 12, (2023) 121602, arXiv:2306.03868 [hep-th]

    work page arXiv 2023

  4. [4]

    Localization of the Free Energy in Supergravity,

    P. Benetti Genolini, J. P. Gauntlett, Y. Jiao, A. L¨ uscher, and J. Sparks, “Localization of the Free Energy in Supergravity,” Phys. Rev. Lett. 133 no. 14, (2024) 141601, arXiv:2407.02554 [hep-th]

    work page arXiv 2024

  5. [5]

    Toric gravitational instantons in gauged supergravity,

    P. Benetti Genolini, J. P. Gauntlett, Y. Jiao, A. L¨ uscher, and J. Sparks, “Toric gravitational instantons in gauged supergravity,” Phys. Rev. D 111 no. 4, (2025) 046024, arXiv:2410.19036 [hep-th]

    work page arXiv 2025

  6. [6]

    Equivariant localization for D = 4 gauged supergravity,

    P. Benetti Genolini, J. P. Gauntlett, Y. Jiao, A. L¨ uscher, and J. Sparks, “Equivariant localization for D = 4 gauged supergravity,” arXiv:2412.07828 [hep-th]

    work page arXiv

  7. [7]

    Localization of the action in AdS/CFT,

    P. Benetti Genolini, J. M. Perez Ipi˜ na, and J. Sparks, “Localization of the action in AdS/CFT,” JHEP 10 (2019) 252, arXiv:1906.11249 [hep-th]

    work page arXiv 2019

  8. [8]

    Kaluza-Klein Monopole,

    R. D. Sorkin, “Kaluza-Klein Monopole,” Phys. Rev. Lett. 51 (1983) 87–90. 59

    work page 1983

  9. [9]

    Magnetic Monopoles in Kaluza-Klein Theories,

    D. J. Gross and M. J. Perry, “Magnetic Monopoles in Kaluza-Klein Theories,” Nucl. Phys. B 226 (1983) 29–48

    work page 1983

  10. [10]

    The holographic supersymmetric Casimir energy

    P. Benetti Genolini, D. Cassani, D. Martelli, and J. Sparks, “The holographic supersymmetric Casimir energy,” Phys. Rev. D 95 no. 2, (2017) 021902, arXiv:1606.02724 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  11. [11]

    Holographic renormalization and supersymmetry

    P. Benetti Genolini, D. Cassani, D. Martelli, and J. Sparks, “Holographic renormalization and supersymmetry,” JHEP 02 (2017) 132, arXiv:1612.06761 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  12. [12]

    The Casimir Energy in Curved Space and its Supersymmetric Counterpart

    B. Assel, D. Cassani, L. Di Pietro, Z. Komargodski, J. Lorenzen, and D. Martelli, “The Casimir Energy in Curved Space and its Supersymmetric Counterpart,” JHEP 07 (2015) 043, arXiv:1503.05537 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  13. [13]

    Microscopic origin of the Bekenstein-Hawking entropy of supersymmetricAdS 5 black holes,

    A. Cabo-Bizet, D. Cassani, D. Martelli, and S. Murthy, “Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS 5 black holes,” JHEP 10 (2019) 062, arXiv:1810.11442 [hep-th]

    work page arXiv 2019

  14. [14]

    A note on the entropy of rotating BPS AdS 7ˆ S4 black holes,

    S. M. Hosseini, K. Hristov, and A. Zaffaroni, “A note on the entropy of rotating BPS AdS7 × S4 black holes,” JHEP 05 (2018) 121, arXiv:1803.07568 [hep-th]

    work page arXiv 2018

  15. [15]

    Localization of the 5D supergravity action and Euclidean saddles for the black hole index,

    D. Cassani, A. Ruip´ erez, and E. Turetta, “Localization of the 5D supergravity action and Euclidean saddles for the black hole index,” JHEP 12 (2024) 086, arXiv:2409.01332 [hep-th]

    work page arXiv 2024

  16. [16]

    Localization of Chern-Simons type invariants of Riemannian foliations

    O. Goertsches, H. Nozawa, and D. Toeben, “Localization of Chern-Simons type invariants of Riemannian foliations,” arXiv:1508.07973 [math.DG]

    work page internal anchor Pith review Pith/arXiv arXiv

  17. [17]

    Colombo, V

    E. Colombo, V. Dimitrov, D. Martelli, and A. Zaffaroni, “Equivariant localization in supergravity in odd dimensions,” arXiv:2502.15624 [hep-th]

    work page arXiv

  18. [18]

    Equivariant localization and holography,

    D. Martelli and A. Zaffaroni, “Equivariant localization and holography,” Lett. Math. Phys. 114 no. 1, (2024) 15, arXiv:2306.03891 [hep-th]

    work page arXiv 2024

  19. [19]

    Equivariant volume extremization and holography,

    E. Colombo, F. Faedo, D. Martelli, and A. Zaffaroni, “Equivariant volume extremization and holography,” JHEP 01 (2024) 095, arXiv:2309.04425 [hep-th]

    work page arXiv 2024

  20. [20]

    An extremization principle for the entropy of rotating BPS black holes in AdS$_5$

    S. M. Hosseini, K. Hristov, and A. Zaffaroni, “An extremization principle for the entropy of rotating BPS black holes in AdS 5,” JHEP 07 (2017) 106, arXiv:1705.05383 [hep-th] . 60

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  21. [21]

    Superconformal indices at large N and the entropy of AdS 5 × SE5 black holes,

    F. Benini, E. Colombo, S. Soltani, A. Zaffaroni, and Z. Zhang, “Superconformal indices at large N and the entropy of AdS 5 × SE5 black holes,” Class. Quant. Grav. 37 no. 21, (2020) 215021, arXiv:2005.12308 [hep-th]

    work page arXiv 2020

  22. [22]

    Localization and attraction,

    P. Benetti Genolini, J. P. Gauntlett, Y. Jiao, A. L¨ uscher, and J. Sparks, “Localization and attraction,” JHEP 05 (2024) 152, arXiv:2401.10977 [hep-th]

    work page arXiv 2024

  23. [23]

    The Holography of F-maximization

    D. Z. Freedman and S. S. Pufu, “The holography of F -maximization,” JHEP 03 (2014) 135, arXiv:1302.7310 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  24. [24]

    All supersymmetric solutions of minimal gauged supergravity in five dimensions

    J. P. Gauntlett and J. B. Gutowski, “All supersymmetric solutions of minimal gauged supergravity in five-dimensions,” Phys. Rev. D 68 (2003) 105009, arXiv:hep-th/0304064. [Erratum: Phys.Rev.D 70, 089901 (2004)]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  25. [25]

    General supersymmetric AdS5 black holes

    J. B. Gutowski and H. S. Reall, “General supersymmetric AdS(5) black holes,” JHEP 04 (2004) 048, arXiv:hep-th/0401129

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  26. [26]

    Holography for ${\cal N}=2^*$ on $S^4$

    N. Bobev, H. Elvang, D. Z. Freedman, and S. S. Pufu, “Holography for N = 2∗ on S4,” JHEP 07 (2014) 001, arXiv:1311.1508 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  27. [27]

    Holography for $\mathcal{N}=1^*$ on $S^4$

    N. Bobev, H. Elvang, U. Kol, T. Olson, and S. S. Pufu, “Holography for N = 1∗ on S4,” JHEP 10 (2016) 095, arXiv:1605.00656 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  28. [28]

    Supersymmetric spindles,

    P. Ferrero, J. P. Gauntlett, and J. Sparks, “Supersymmetric spindles,” JHEP 01 (2022) 102, arXiv:2112.01543 [hep-th]

    work page arXiv 2022

  29. [29]

    Supercurrent anomalies in 4d SCFTs

    I. Papadimitriou, “Supercurrent anomalies in 4d SCFTs,” JHEP 07 (2017) 038, arXiv:1703.04299 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  30. [30]

    Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization

    O. S. An, “Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization,” JHEP 12 (2017) 107, arXiv:1703.09607 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  31. [31]

    Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity

    I. Papadimitriou, “Supersymmetry anomalies in N = 1 conformal supergravity,” JHEP 04 (2019) 040, arXiv:1902.06717 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  32. [32]

    ’t Hooft anomalies and the holomorphy of supersymmetric partition functions,

    C. Closset, L. Di Pietro, and H. Kim, “’t Hooft anomalies and the holomorphy of supersymmetric partition functions,” JHEP 08 (2019) 035, arXiv:1905.05722 [hep-th] . 61

    work page arXiv 2019

  33. [33]

    Comments on Anomalies in Supersymmetric Theories,

    S. M. Kuzenko, A. Schwimmer, and S. Theisen, “Comments on Anomalies in Supersymmetric Theories,” J. Phys. A 53 no. 6, (2020) 064003, arXiv:1909.07084 [hep-th]

    work page arXiv 2020

  34. [34]

    Consistency of supersymmetric ’t Hooft anomalies,

    A. Bzowski, G. Festuccia, and V. Proch´ azka, “Consistency of supersymmetric ’t Hooft anomalies,” JHEP 02 (2021) 225, arXiv:2011.09978 [hep-th]

    work page arXiv 2021

  35. [35]

    Supersymmetric AdS_4 black holes and attractors

    S. L. Cacciatori and D. Klemm, “Supersymmetric AdS(4) black holes and attractors,” JHEP 01 (2010) 085, arXiv:0911.4926 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  36. [36]

    Large AdS black holes from QFT,

    S. Choi, J. Kim, S. Kim, and J. Nahmgoong, “Large AdS black holes from QFT,” arXiv:1810.12067 [hep-th]

    work page arXiv

  37. [37]

    Black holes in 4dN= 4 Super Yang-Mills from field theory,

    F. Benini and E. Milan, “Black Holes in 4D N =4 Super-Yang-Mills Field Theory,” Phys. Rev. X 10 no. 2, (2020) 021037, arXiv:1812.09613 [hep-th]

    work page arXiv 2020

  38. [38]

    A gravity interpretation for the Bethe Ansatz expansion of the N = 4 SYM index,

    O. Aharony, F. Benini, O. Mamroud, and E. Milan, “A gravity interpretation for the Bethe Ansatz expansion of the N = 4 SYM index,” Phys. Rev. D 104 (2021) 086026, arXiv:2104.13932 [hep-th]

    work page arXiv 2021

  39. [39]

    Mass of Rotating Black Holes in Gauged Supergravities

    W. Chen, H. Lu, and C. N. Pope, “Mass of rotating black holes in gauged supergravities,” Phys. Rev. D 73 (2006) 104036, arXiv:hep-th/0510081

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  40. [40]

    The gravity dual of supersymmetric gauge theories on a squashed $S^1 \times S^3$

    D. Cassani and D. Martelli, “The gravity dual of supersymmetric gauge theories on a squashed S 1 x S3,” JHEP 08 (2014) 044, arXiv:1402.2278 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  41. [41]

    Localization on Hopf surfaces

    B. Assel, D. Cassani, and D. Martelli, “Localization on Hopf surfaces,” JHEP 08 (2014) 123, arXiv:1405.5144 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  42. [42]

    Gravity duals of supersymmetric gauge theories on three-manifolds

    D. Farquet, J. Lorenzen, D. Martelli, and J. Sparks, “Gravity duals of supersymmetric gauge theories on three-manifolds,” JHEP 08 (2016) 080, arXiv:1404.0268 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  43. [43]

    Supersymmetric AdS5 black holes

    J. B. Gutowski and H. S. Reall, “Supersymmetric AdS(5) black holes,” JHEP 02 (2004) 006, arXiv:hep-th/0401042

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  44. [44]

    General Non-Extremal Rotating Black Holes in Minimal Five-Dimensional Gauged Supergravity

    Z. W. Chong, M. Cvetic, H. Lu, and C. N. Pope, “General non-extremal rotating black holes in minimal five-dimensional gauged supergravity,” Phys. Rev. Lett. 95 (2005) 161301, arXiv:hep-th/0506029

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  45. [45]

    Rotating attractors and BPS black holes in AdS4,

    K. Hristov, S. Katmadas, and C. Toldo, “Rotating attractors and BPS black holes in AdS4,” JHEP 01 (2019) 199, arXiv:1811.00292 [hep-th] . 62

    work page arXiv 2019

  46. [46]

    Gluing gravitational blocks for AdS black holes,

    S. M. Hosseini, K. Hristov, and A. Zaffaroni, “Gluing gravitational blocks for AdS black holes,” JHEP 12 (2019) 168, arXiv:1909.10550 [hep-th]

    work page arXiv 2019

  47. [47]

    Supersymmetric multi-charge AdS_5 black holes

    H. K. Kunduri, J. Lucietti, and H. S. Reall, “Supersymmetric multi-charge AdS(5) black holes,” JHEP 04 (2006) 036, arXiv:hep-th/0601156

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  48. [48]

    Charged Rotating Black Holes in Five Dimensional U(1)^3 Gauged N=2 Supergravity

    M. Cvetic, H. Lu, and C. N. Pope, “Charged rotating black holes in five dimensional U(1)3 gauged N=2 supergravity,” Phys. Rev. D 70 (2004) 081502, arXiv:hep-th/0407058

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  49. [49]

    Rotating Black Holes in Gauged Supergravities; Thermodynamics, Supersymmetric Limits, Topological Solitons and Time Machines

    M. Cvetic, G. W. Gibbons, H. Lu, and C. N. Pope, “Rotating black holes in gauged supergravities: Thermodynamics, supersymmetric limits, topological solitons and time machines,” arXiv:hep-th/0504080

    work page internal anchor Pith review Pith/arXiv arXiv

  50. [50]

    The BPS limit of rotating AdS black hole thermodynamics,

    D. Cassani and L. Papini, “The BPS limit of rotating AdS black hole thermodynamics,” JHEP 09 (2019) 079, arXiv:1906.10148 [hep-th]

    work page arXiv 2019

  51. [51]

    I. Arav, J. P. Gauntlett, M. M. Roberts, and C. Rosen To appear

    work page

  52. [52]

    Cassani and S

    D. Cassani and S. Murthy, Quantum black holes: supersymmetry and exact results. 2, 2025. arXiv:2502.15360 [hep-th]

    work page arXiv 2025

  53. [53]

    Gauged supergravity from type IIB string theory on Y^{p,q} manifolds

    A. Buchel and J. T. Liu, “Gauged supergravity from type IIB string theory on Y p,q manifolds,” Nucl. Phys. B 771 (2007) 93–112, arXiv:hep-th/0608002

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  54. [54]

    Supersymmetric AdS_5 solutions of M-theory

    J. P. Gauntlett, D. Martelli, J. Sparks, and D. Waldram, “Supersymmetric AdS(5) solutions of M theory,” Class. Quant. Grav. 21 (2004) 4335–4366, arXiv:hep-th/0402153

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  55. [55]

    Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions

    J. P. Gauntlett and O. Varela, “Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions,” Phys. Rev. D 76 (2007) 126007, arXiv:0707.2315 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  56. [56]

    Embedding AdS Black Holes in Ten and Eleven Dimensions

    M. Cvetic, M. J. Duff, P. Hoxha, J. T. Liu, H. Lu, J. X. Lu, R. Martinez-Acosta, C. N. Pope, H. Sati, and T. A. Tran, “Embedding AdS black holes in ten-dimensions and eleven-dimensions,” Nucl. Phys. B 558 (1999) 96–126, arXiv:hep-th/9903214

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  57. [57]

    Black hole thermodynamics at 4 derivatives, natural variables and BPS limits,

    K. Hristov, P.-J. Hu, and Y. Pang, “Black hole thermodynamics at 4 derivatives, natural variables and BPS limits,” arXiv:2505.22726 [hep-th]

    work page arXiv

  58. [58]

    Black Hole Entropy is Noether Charge

    R. M. Wald, “Black hole entropy is the Noether charge,” Phys. Rev. D 48 no. 8, (1993) R3427–R3431, arXiv:gr-qc/9307038. 63

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  59. [59]

    Euclidean N=2 Supergravity

    J. B. Gutowski and W. A. Sabra, “Euclidean N=2 Supergravity,” Phys. Lett. B 718 (2012) 610–614, arXiv:1209.2029 [hep-th] . 64

    work page internal anchor Pith review Pith/arXiv arXiv 2012