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Proposal for symmetry topological field theories and symmetry theories from holography

Francesco Mignosa* and Diego Rodriguez-Gomez†

  • *Contact author: francesco.mignosa02@gmail.com
  • †Contact author: d.rodriguez.gomez@uniovi.es

Phys. Rev. D 112, 106016 – Published 24 November, 2025

DOI: https://doi.org/10.1103/ms8g-sckd

Abstract

We propose an embedding of the symmetry topological field theory (symTFT) construction in (finite cutoff) holography. The proposal passes several nontrivial consistency checks reproducing the expected symTFTs in various cases, including the recently discussed symTFT for the 1-form symmetry of 4D N=4 super Yang-Mills (SYM). Moreover, we comment on the possibility of unifying the symTFT and the symmetry theory (symTh) descriptions via the democratic formulation of supergravity, using the 4d N=4 SYM theory as an example.

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References (31)

  1. D. S. Freed and C. Teleman, Relative quantum field theory, Commun. Math. Phys. 326, 459 (2014).
  2. F. Apruzzi, F. Bonetti, I. García Etxebarria, S. S. Hosseini, and S. Schafer-Nameki, Symmetry TFTs from string theory, Commun. Math. Phys. 402, 895 (2023).
  3. F. Bonetti, M. Del Zotto, and R. Minasian, SymTFTs for continuous non-Abelian symmetries, arXiv:2402.12347.
  4. R. Argurio, F. Benini, M. Bertolini, G. Galati, and P. Niro, On the symmetry TFT of Yang-Mills-Chern-Simons theory, J. High Energy Phys. 07 (2024) 130.
  5. M. Cvetič, R. Donagi, J. J. Heckman, M. Hübner, and E. Torres, Cornering relative symmetry theories, Phys. Rev. D 111, 085026 (2025).
  6. X. Yu, Gauging in parameter space: A top-down perspective, Phys. Rev. D 112, 025020 (2025).
  7. F. Gagliano and I. García Etxebarria, SymTFTs for U(1) symmetries from descent, arXiv:2411.15126.
  8. F. Apruzzi, F. Bedogna, and N. Dondi, SymTh for non-finite symmetries, arXiv:2402.14813.
  9. E. Witten, SL(2,Z) action on three-dimensional conformal field theories with Abelian symmetry, arXiv:hep-th/0307041.
  10. D. Marolf and S. F. Ross, Boundary conditions and new dualities: Vector fields in AdS/CFT, J. High Energy Phys. 11 (2006) 085.
  11. O. DeWolfe and K. Higginbotham, Generalized symmetries and 2-groups via electromagnetic duality in AdS/CFT, Phys. Rev. D 103, 026011 (2021).
  12. I. Heemskerk and J. Polchinski, Holographic and Wilsonian renormalization groups, J. High Energy Phys. 06 (2011) 031.
  13. J. de Boer, E. P. Verlinde, and H. L. Verlinde, On the holographic renormalization group, J. High Energy Phys. 08 (2000) 003.
  14. T. Faulkner, H. Liu, and M. Rangamani, Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm, J. High Energy Phys. 08 (2011) 051.
  15. L. McGough, M. Mezei, and H. Verlinde, Moving the CFT into the bulk with TT¯, J. High Energy Phys. 04 (2018) 010.
  16. M. Taylor, TT¯ deformations in general dimensions, Adv. Theor. Math. Phys. 27, 37 (2023).
  17. T. Hartman, J. Kruthoff, E. Shaghoulian, and A. Tajdini, Holography at finite cutoff with a T2 deformation, J. High Energy Phys. 03 (2019) 004.
  18. A. Antinucci and F. Benini, Anomalies and gauging of U(1) symmetries, Phys. Rev. B 111, 2 (2025).
  19. M. Rocek and E. P. Verlinde, Duality, quotients, and currents, Nucl. Phys. B373, 630 (1992).
  20. O. Bergman, E. Garcia-Valdecasas, F. Mignosa, and D. Rodriguez-Gomez, The SymTFT of u(N) Yang-Mills theory and holography, arXiv:2508.00992.
  21. J. M. Maldacena, G. W. Moore, and N. Seiberg, D-brane charges in five-brane backgrounds, J. High Energy Phys. 10 (2001) 005.
  22. O. Evnin, E. Joung, and K. Mkrtchyan, Democratic Lagrangians from topological bulk, Phys. Rev. D 109, 066003 (2024).
  23. J. J. Heckman, M. Hübner, and C. Murdia, On the holographic dual of a topological symmetry operator, Phys. Rev. D 110, 046007 (2024).
  24. J. J. Heckman, M. Hübner, and C. Murdia, Symmetry theories, Wigner’s function, compactification, and holography, arXiv:2505.23887.
  25. F. Apruzzi, N. Dondi, I. García Etxebarria, H. T. Lam, and S. Schafer-Nameki, Symmetry TFTs for continuous spacetime symmetries, arXiv:2509.07965.
  26. F. Bonetti, M. Del Zotto, and R. Minasian, SymTFT for continuous symmetries: Non-linear realizations and spontaneous breaking, arXiv:2509.10343.
  27. A. Baguet, O. Hohm, and H. Samtleben, Consistent Type IIB reductions to maximal 5D supergravity, Phys. Rev. D 92, 065004 (2015).
  28. E. Witten, AdS/CFT correspondence and topological field theory, J. High Energy Phys. 12 (1998) 012.
  29. O. Bergman, E. Garcia-Valdecasas, F. Mignosa, and D. Rodriguez-Gomez, Non-BPS branes and continuous symmetries, J. High Energy Phys. 02 (2025) 066.
  30. H. Calvo, F. Mignosa, and D. Rodriguez-Gomez, Continuous symmetry defects and brane/anti-brane systems, J. High Energy Phys. 06 (2025) 196.
  31. H. Calvo, F. Mignosa, and D. Rodriguez-Gomez, R-symmetries, anomalies and non-invertible defects from non-BPS branes, arXiv:2506.13859.

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