- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

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

On the holographic dual of a symmetry operator at finite temperature

Jonathan J. Heckman1,2,*, Max Hübner3,†, and Chitraang Murdia1,‡

  • *Contact author: jheckman@sas.upenn.edu
  • †Contact author: max-elliot.huebner@physics.uu.se
  • ‡Contact author: murdia@sas.upenn.edu
PDF

Phys. Rev. D 112, 126010 – Published 15 December, 2025

DOI: https://doi.org/10.1103/sg2d-frj1

Abstract

Topological symmetry operators of holographic large N CFTD’s are dual to dynamical branes in the gravity dual AdSD+1. We use this correspondence to establish a dictionary between thermal expectation values of symmetry operators in the Euclidean CFTD and the evaluation of gravitational saddles in the presence of a dynamical brane. Expectation values of 0-form symmetry operators in the CFTD are then related to branes wrapped on volume minimizing cycles in the bulk, i.e., the Euclidean continuation of a black hole horizon. We illustrate with some representative examples, including gravity in AdS3, duality/triality defects in four-dimensional N=4 super Yang-Mills theory, and the dual of R-symmetry operators probing five-dimensional Bogomol’nyi–Prasad–Sommerfield black holes.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (56)

  1. D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, Generalized global symmetries, J. High Energy Phys. 02 (2015) 172.
  2. J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1998).
  3. F. Apruzzi, I. Bah, F. Bonetti, and S. Schafer-Nameki, Non-invertible symmetries from holography and branes, Phys. Rev. Lett. 130, 121601 (2023).
  4. I. Garcia Etxebarria, Branes and non-invertible symmetries, Fortschr. Phys. 70, 2200154 (2022).
  5. J. J. Heckman, M. Hübner, E. Torres, and H. Y. Zhang, The branes behind generalized symmetry operators, Fortschr. Phys. 71, 2200180 (2023).
  6. J. J. Heckman, M. Hübner, E. Torres, X. Yu, and H. Y. Zhang, Top down approach to topological duality defects, Phys. Rev. D 108, 046015 (2023).
  7. J. J. Heckman, M. Hübner, and C. Murdia, On the holographic dual of a topological symmetry operator, Phys. Rev. D 110, 046007 (2024).
  8. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428, 105 (1998).
  9. T. Banks, M. R. Douglas, G. T. Horowitz, and E. J. Martinec, AdS dynamics from conformal field theory, arXiv:hep-th/9808016.
  10. S. W. Hawking and D. N. Page, Thermodynamics of black holes in anti-de Sitter space, Commun. Math. Phys. 87, 577 (1983).
  11. E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2, 505 (1998).
  12. M. Cvetič and S. S. Gubser, Phases of R-charged black holes, spinning branes and strongly coupled gauge theories, J. High Energy Phys. 04 (1999) 024.
  13. J. D. Bekenstein, Black holes and the second law, Lett. Nuovo Cimento 4, 737 (1972).
  14. J. D. Bekenstein, Generalized second law of thermodynamics in black hole physics, Phys. Rev. D 9, 3292 (1974).
  15. S. W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43, 199 (1975); 46, 206(E) (1976).
  16. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96, 181602 (2006).
  17. V. E. Hubeny, M. Rangamani, and T. Takayanagi, A covariant holographic entanglement entropy proposal, J. High Energy Phys. 07 (2007) 062.
  18. A. Maloney and E. Witten, Quantum gravity partition functions in three dimensions, J. High Energy Phys. 02 (2010) 029.
  19. J. Kaidi, K. Ohmori, and Y. Zheng, Kramers-Wannier-like duality defects in (3+1)d gauge theories, Phys. Rev. Lett. 128, 111601 (2022).
  20. Y. Choi, C. Cordova, P.-S. Hsin, H. T. Lam, and S.-H. Shao, Non-invertible condensation, duality, and triality defects in 3+1 dimensions, Commun. Math. Phys. 402, 489 (2023).
  21. V. Bashmakov, M. Del Zotto, A. Hasan, and J. Kaidi, Non-invertible symmetries of class S theories, J. High Energy Phys. 05 (2023) 225.
  22. M. Del Zotto, S. N. Meynet, and R. Moscrop, Remarks on geometric engineering, symmetry TFTs and anomalies, J. High Energy Phys. 07 (2024) 220.
  23. M. R. Gaberdiel and B. Zwiebach, Exceptional groups from open strings, Nucl. Phys. B518, 151 (1998).
  24. O. DeWolfe, T. Hauer, A. Iqbal, and B. Zwiebach, Uncovering the symmetries on [p,q] seven-branes: Beyond the Kodaira classification, Adv. Theor. Math. Phys. 3, 1785 (1999).
  25. J. B. Gutowski and H. S. Reall, Supersymmetric AdS5 black holes, J. High Energy Phys. 02 (2004) 006.
  26. J. B. Gutowski and H. S. Reall, General supersymmetric AdS5 black holes, J. High Energy Phys. 04 (2004) 048.
  27. Z. W. Chong, M. Cvetič, H. Lu, and C. N. Pope, Five-dimensional gauged supergravity black holes with independent rotation parameters, Phys. Rev. D 72, 041901 (2005).
  28. H. K. Kunduri, J. Lucietti, and H. S. Reall, Supersymmetric multi-charge AdS5 black holes, J. High Energy Phys. 04 (2006) 036.
  29. S. M. Hosseini, K. Hristov, and A. Zaffaroni, An extremization principle for the entropy of rotating BPS black holes in AdS5, J. High Energy Phys. 07 (2017) 106.
  30. A. Cabo-Bizet, D. Cassani, D. Martelli, and S. Murthy, Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes, J. High Energy Phys. 10 (2019) 062.
  31. S. Choi, J. Kim, S. Kim, and J. Nahmgoong, Large AdS black holes from QFT, arXiv:1810.12067.
  32. F. Benini and E. Milan, Black holes in 4D N=4 super-Yang-Mills field theory, Phys. Rev. X 10, 021037 (2020).
  33. A. Zaffaroni, AdS black holes, holography and localization, Living Rev. Relativity 23, 2 (2020).
  34. A. Cabo-Bizet, D. Cassani, D. Martelli, and S. Murthy, The asymptotic growth of states of the 4d N=1 superconformal index, J. High Energy Phys. 08 (2019) 120.
  35. A. Cabo-Bizet, D. Cassani, D. Martelli, and S. Murthy, The large-N limit of the 4d N=1 superconformal index, J. High Energy Phys. 11 (2020) 150.
  36. F. Benini, E. Colombo, S. Soltani, A. Zaffaroni, and Z. Zhang, Superconformal indices at large N and the entropy of AdS5×SE5 black holes, Classical Quantum Gravity 37, 215021 (2020).
  37. H. Ooguri, A. Strominger, and C. Vafa, Black hole attractors and the topological string, Phys. Rev. D 70, 106007 (2004).
  38. A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, J. High Energy Phys. 09 (2005) 038.
  39. A. Sen, Quantum entropy function from AdS2/CFT1 correspondence, Int. J. Mod. Phys. A 24, 4225 (2009).
  40. A. Sen, Arithmetic of quantum entropy function, J. High Energy Phys. 08 (2009) 068.
  41. M. Cvetič, J. J. Heckman, M. Hübner, and C. Murdia, Metric isometries, holography, and continuous symmetry operators, arXiv:2501.17911.
  42. I. Arav, J. P. Gauntlett, Y. Jiao, M. M. Roberts, and C. Rosen, Superconformal monodromy defects in N=4 SYM and LS theory, J. High Energy Phys. 08 (2024) 177.
  43. O. Aharony, E. Y. Urbach, and M. Weiss, Generalized Hawking-Page transitions, J. High Energy Phys. 08 (2019) 018.
  44. J. M. Maldacena, Eternal black holes in anti-de Sitter, J. High Energy Phys. 04 (2003) 021.
  45. V. Balasubramanian, M. J. Kang, C. Murdia, and S. F. Ross, Signals of multiparty entanglement and holography, J. High Energy Phys. 06 (2025) 068.
  46. M. R. Douglas and G. W. Moore, D-branes, quivers, and ALE instantons, arXiv:hep-th/9603167.
  47. A. E. Lawrence, N. Nekrasov, and C. Vafa, On conformal field theories in four-dimensions, Nucl. Phys. B533, 199 (1998).
  48. S. Kachru and E. Silverstein, 4-D conformal theories and strings on orbifolds, Phys. Rev. Lett. 80, 4855 (1998).
  49. S. Gukov, M. Rangamani, and E. Witten, Dibaryons, strings and branes in AdS orbifold models, J. High Energy Phys. 12 (1998) 025.
  50. K. Behrndt, M. Cvetič, and W. A. Sabra, Nonextreme black holes of five-dimensional N=2 AdS supergravity, Nucl. Phys. B553, 317 (1999).
  51. K. Behrndt, A. H. Chamseddine, and W. A. Sabra, BPS black holes in N=2 five-dimensional AdS supergravity, Phys. Lett. B 442, 97 (1998).
  52. M. Cvetič and S. S. Gubser, Thermodynamic stability and phases of general spinning branes, J. High Energy Phys. 07 (1999) 010.
  53. A. Chamblin, R. Emparan, C. V. Johnson, and R. C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60, 064018 (1999).
  54. R. C. Myers and O. Tafjord, Superstars and giant gravitons, J. High Energy Phys. 11 (2001) 009.
  55. A. Buchel and L. A. Pando Zayas, Hagedorn versus Hawking-Page transition in string theory, Phys. Rev. D 68, 066012 (2003).
  56. S. S. Gubser and J. J. Heckman, Thermodynamics of R-charged black holes in AdS5 from effective strings, J. High Energy Phys. 11 (2004) 052.

Outline

Information

Phys. Rev. D 112, 126010– Published 15 December, 2025
  • Received 3 June 2025
  • Accepted 7 October 2025
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