- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Equivariant Localization for Higher Derivative Supergravity

Pietro Benetti Genolini1, Florian Gaar2, Jerome P. Gauntlett3, and James Sparks2

PDF

Phys. Rev. Lett. 137, 111602 – Published 11 September, 2026

DOI: https://doi.org/10.1103/9bys-f6s6

Abstract

Conformal supergravity provides an effective off-shell formalism to study higher derivative actions. We show that the D=4, N=2 theory admits equivariantly closed forms. These may be used to compute closed-form expressions for supersymmetric observables in a general class of supergravity theories with higher derivative couplings, without any need to solve equations of motion. We discuss applications to holography, presenting results for on-shell actions that are conjecturally valid to all orders in the perturbative 1/N expansion.

View figure in article

Physics Subject Headings (PhySH)

See Also

Probing black holes with equivariant localization

Pietro Benetti Genolini, Christopher Couzens, and Alice Lüscher
Phys. Rev. D 114, 066004 (2026)

Article Text

References (37)

  1. P. Benetti Genolini, J. P. Gauntlett, and J. Sparks, Equivariant localization in supergravity, Phys. Rev. Lett. 131, 121602 (2023).
  2. T. Mohaupt, Black hole entropy, special geometry and strings, Fortschr. Phys. 49, 3 (2001).
  3. I. Mandal and A. Sen, Black hole microstate counting and its macroscopic counterpart, Classical Quantum Gravity 27, 214003 (2010).
  4. N. Bobev, A. M. Charles, K. Hristov, and V. Reys, The unreasonable effectiveness of higher-derivative supergravity in AdS4 holography, Phys. Rev. Lett. 125, 131601 (2020).
  5. N. Bobev, A. M. Charles, K. Hristov, and V. Reys, Higher-derivative supergravity, AdS4 holography, and black holes, J. High Energy Phys. 08 (2021) 173.
  6. P. Benetti Genolini and P. Richmond, Supersymmetry of higher-derivative supergravity in AdS4 holography, Phys. Rev. D 104, L061902 (2021).
  7. K. Hristov, 4d N=2 supergravity observables from Nekrasov-like partition functions, J. High Energy Phys. 02 (2022) 079.
  8. K. Hristov, ABJM at finite N via 4d supergravity, J. High Energy Phys. 10 (2022) 190.
  9. N. Bobev, J. Hong, and V. Reys, Large N partition functions of the ABJM theory, J. High Energy Phys. 02 (2023) 020.
  10. K. Hristov, Equivariant localization and gluing rules in 4d N=2 higher derivative supergravity, in 2024 MATRIX Annals, Part I (Springer, Cham, 2026).
  11. N. Berline and M. Vergne, Classes caractéristiques équivariantes. Formules de localisation en cohomologie équivariante, C. R. Acad. Sci. Paris 295, 539 (1982).
  12. M. F. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23, 1 (1984).
  13. P. Benetti Genolini, F. Gaar, J. P. Gauntlett, and J. Sparks, Equivariant localization for conformal supergravity (to be published).
  14. F. Gaar, J. P. Gauntlett, J. Park, and J. Sparks, Superconformal index and localizing higher derivative supergravity, Phys. Rev. D 114, L021904 (2026).
  15. B. de Wit and V. Reys, Euclidean supergravity, J. High Energy Phys. 12 (2017) 011.
  16. D. Freedman and A. van Proeyen, Supergravity (Cambridge University Press, Cambridge, England, 2012), pp. 1–607.
  17. E. Lauria and A. Van Proeyen, N=2 supergravity in D=4, 5, 6 dimensions, in Lecture Notes in Physics (Springer, Cham, 2020), Vol. 966.
  18. D. Butter, B. de Wit, S. M. Kuzenko, and I. Lodato, New higher-derivative invariants in N=2 supergravity and the Gauss-Bonnet term, J. High Energy Phys. 12 (2013) 062.

  19. The symplectic Majorana condition on a spinor εi is εi*=Cϵijεj, where C is the charge conjugation matrix.

  20. C. Klare and A. Zaffaroni, Extended supersymmetry on curved spaces, J. High Energy Phys. 10 (2013) 218.
  21. G. W. Gibbons and S. W. Hawking, Classification of gravitational instanton symmetries, Commun. Math. Phys. 66, 291 (1979).

  22. The generalization to orbifolds is straightforward.

  23. P. Benetti Genolini, J. P. Gauntlett, Y. Jiao, A. Lüscher, and J. Sparks, Localization of the free energy in supergravity, Phys. Rev. Lett. 133, 141601 (2024).
  24. P. Benetti Genolini, J. P. Gauntlett, Y. Jiao, A. Lüscher, and J. Sparks, Toric gravitational instantons in gauged supergravity, Phys. Rev. D 111, 046024 (2025).
  25. P. Benetti Genolini, J. P. Gauntlett, Y. Jiao, A. Lüscher, and J. Sparks, Equivariant localization for D=4 gauged supergravity, J. High Energy Phys. 08 (2025) 211.

  26. The extension to Σ being a spindle is straightforward.

  27. S. M. Hosseini, K. Hristov, and A. Zaffaroni, Gluing gravitational blocks for AdS black holes, J. High Energy Phys. 12 (2019) 168.
  28. N. Bobev, A. M. Charles, and V. S. Min, Euclidean black saddles and AdS4 black holes, J. High Energy Phys. 10 (2020) 073.
  29. J. W. York, Jr., Role of conformal three geometry in the dynamics of gravitation, Phys. Rev. Lett. 28, 1082 (1972).
  30. G. W. Gibbons and S. W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15, 2752 (1977).
  31. R. C. Myers, Higher derivative gravity, surface terms and string theory, Phys. Rev. D 36, 392 (1987).
  32. O. Aharony, O. Bergman, D. L. Jafferis, and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, J. High Energy Phys. 10 (2008) 091.
  33. M. Cvetič, M. J. Duff, P. Hoxha, J. T. Liu, H. Lü, J. X. Lu, R. Martinez-Acosta, C. N. Pope, H. Sati, and T. A. Tran, Embedding AdS black holes in ten and eleven dimensions, Nucl. Phys. B558, 96 (1999).

  34. This general class of rigid supersymmetric geometries was studied in [35].

  35. C. Closset, T. T. Dumitrescu, G. Festuccia, and Z. Komargodski, Supersymmetric field theories on three-manifolds, J. High Energy Phys. 05 (2013) 017.
  36. C. Closset and H. Kim, Three-dimensional N=2 supersymmetric gauge theories and partition functions on Seifert manifolds: A review, Int. J. Mod. Phys. A 34, 1930011 (2019).
  37. J. Hong, Perturbatively exact supersymmetric partition functions of ABJM theory on Seifert manifolds and holography, J. High Energy Phys. 01 (2025) 194.

Outline

Information

Phys. Rev. Lett. 137, 111602– Published 11 September, 2026
  • Received 14 May 2026
  • Accepted 4 August 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation