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Gauging in parameter space: A top-down perspective

Xingyang Yu*

  • Physics Department, Robeson Hall, Virginia Tech, Blacksburg, Virginia 24061, USA

  • *Contact author: xingyangy@vt.edu

Phys. Rev. D 112, 025020 – Published 31 July, 2025

DOI: https://doi.org/10.1103/638n-qwnm

Abstract

In this paper, we discuss a novel top-down perspective on gauging parameters in quantum field theories (QFTs) by promoting them to partially dynamical fields. Through a generalized notion of symmetry theories, we explore the consequences of this promotion, revealing new topological defects, decompositions as well as generalized symmetry structures across various dimensions. We provide a systematic top-down derivation of symmetry theories for parameters and discuss how special types of branes, such as Euclidean branes and fluxbranes are related to gauging in the parameter space in QFTs. We illustrate our theoretical framework with two key examples: the modified instanton sum in 4D N=4 super Yang-Mills theory and the gauging of gauge ranks in 3D ABJ(M) theories.

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References (62)

  1. Nathan Seiberg, The power of holomorphy: Exact results in 4-D SUSY field theories, in Particles, Strings, and Cosmology (PASCOS 94) (1994), pp. 0357–369.
  2. Simeon Hellerman, Andre Henriques, Tony Pantev, Eric Sharpe, and Matt Ando, Cluster decomposition, T-duality, and gerby CFT’s, Adv. Theor. Math. Phys. 11, 751 (2007).
  3. Eric Sharpe, An introduction to decomposition, in 2021-2022 MATRIX Annals. MATRIX Book Series (Springer, Cham, 2022).
  4. Yuya Tanizaki and Mithat Ünsal, Modified instanton sum in QCD and higher-groups, J. High Energy Phys. 03 (2020) 123.
  5. Zohar Komargodski, Kantaro Ohmori, Konstantinos Roumpedakis, and Sahand Seifnashri, Symmetries and strings of adjoint QCD2, J. High Energy Phys. 03 (2021) 103.
  6. Davide Gaiotto, Anton Kapustin, Nathan Seiberg, and Brian Willett, Generalized global symmetries, J. High Energy Phys. 02 (2015) 172.
  7. Nathan Seiberg, Modifying the sum over topological sectors and constraints on supergravity, J. High Energy Phys. 07 (2010) 070.
  8. Clay Córdova, Daniel S. Freed, Ho Tat Lam, and Nathan Seiberg, Anomalies in the space of coupling constants and their dynamical applications I, SciPost Phys. 8, 001 (2020).
  9. Clay Córdova, Daniel S. Freed, Ho Tat Lam, and Nathan Seiberg, Anomalies in the space of coupling constants and their dynamical applications II, SciPost Phys. 8, 002 (2020).
  10. Eric Sharpe, Undoing decomposition, Int. J. Mod. Phys. A 34, 1950233 (2020).
  11. Thomas Vandermeulen, Lower-form symmetries, arXiv:2211.04461.
  12. Daniel Aloni, Eduardo García-Valdecasas, Matthew Reece, and Motoo Suzuki, Spontaneously broken (−1)-form U(1) symmetries, SciPost Phys. 17, 031 (2024).
  13. T. Daniel Brennan, Constraints on symmetry-preserving gapped phases from coupling constant anomalies, Phys. Rev. D 110, L041701 (2024).
  14. V. G. Turaev and O. Y. Viro, State sum invariants of 3 manifolds and quantum 6j symbols, Topology 31, 865 (1992).
  15. Fabio Apruzzi, Federico Bonetti, I. García Etxebarria, Saghar S. Hosseini, and Sakura Schafer-Nameki, Symmetry TFTs from string theory, Commun. Math. Phys. 402, 895 (2023).
  16. Daniel S. Freed, Gregory W. Moore, and Constantin Teleman, Topological symmetry in quantum field theory, arXiv:2209.07471.
  17. Daniel S. Freed and Constantin Teleman, Relative quantum field theory, Commun. Math. Phys. 326, 459 (2014).
  18. Iñaki García Etxebarria and Saghar S. Hosseini, Some aspects of symmetry descent, J. High Energy Phys. 12 (2024) 223.
  19. Daniel S. Freed, Gregory W. Moore, and Graeme Segal, Heisenberg groups and noncommutative fluxes, Ann. Phys. (Amsterdam) 322, 236 (2007).
  20. I. Garcia Etxebarria, Ben Heidenreich, and Diego Regalado, IIB flux non-commutativity and the global structure of field theories, J. High Energy Phys. 10 (2019) 169.
  21. T. Daniel Brennan and Zhengdi Sun, A SymTFT for continuous symmetries, J. High Energy Phys. 12 (2024) 100.
  22. Andrea Antinucci and Francesco Benini, Anomalies and gauging of U(1) symmetries, Phys. Rev. B 111, 024110 (2025).
  23. See also [24, 25, 26] for alternative formulations of continuous symmetry theories from string theory.

  24. Fabio Apruzzi, Francesco Bedogna, and Nicola Dondi, SymTh for non-finite symmetries, 2024.
  25. Federico Bonetti, Michele Del Zotto, and Ruben Minasian, SymTFTs for continuous non-abelian symmetries, arXiv:2402.12347.
  26. Mirjam Cvetič, Ron Donagi, Jonathan J. Heckman, Max Hübner, and Ethan Torres, Cornering relative symmetry theories, Phys. Rev. D 111, 085026 (2025).
  27. Fabio Apruzzi, Ibrahima Bah, Federico Bonetti, and Sakura Schafer-Nameki, Noninvertible symmetries from holography and branes, Phys. Rev. Lett. 130, 121601 (2023).
  28. I. Garcia Etxebarria, Branes and non-invertible symmetries, Fortschr. Phys. 70, 2200154 (2022).
  29. Jonathan J. Heckman, Max Hübner, Ethan Torres, and Hao Y. Zhang, The Branes Behind Generalized Symmetry Operators, Fortschr. Phys. 71, 2200180 (2023).
  30. Jonathan J. Heckman, Max Hubner, Ethan Torres, Xingyang Yu, and Hao Y. Zhang, Top down approach to topological duality defects, Phys. Rev. D 108, 046015 (2023).
  31. Edward Witten, On S duality in Abelian gauge theory, Sel. Math. 1, 383 (1995).
  32. We thank I. Garcia Etxebarria for suggesting this name.

  33. Similar limit was also discussed in the context of non-abelian continuous symmetries in [25].

  34. Xingyang Yu, Non-invertible symmetries in 2D from type IIB string theory, Phys. Rev. D 110, 065008 (2024).
  35. Sebastian Franco and Xingyang Yu, Generalized symmetries in 2D from string theory: SymTFTs, intrinsic relativeness, and anomalies of non-invertible symmetries, J. High Energy Phys. 11 (2024) 004.
  36. Michael R. Douglas, Branes within branes, NATO Sci. Ser. C 520, 267 (1999).
  37. Michael Gutperle and Andrew Strominger, Fluxbranes in string theory, J. High Energy Phys. 06 (2001) 035.
  38. Roberto Emparan and Michael Gutperle, From p-branes to fluxbranes and back, J. High Energy Phys. 12 (2001) 023.
  39. Mirjam Cvetič, Jonathan J. Heckman, Max Hübner, and Ethan Torres, Fluxbranes, Generalized Symmetries, and Verlinde’s Metastable Monopole, Phys. Rev. D 109, 046007 (2024).
  40. Another proposal for branes behind U(1) symmetry operators was discussed in [41], where the Wess-Zumino term (10) was identified as the topological sector of non-BPS branes.

  41. Oren Bergman, Eduardo Garcia-Valdecasas, Francesco Mignosa, and Diego Rodriguez-Gomez, Non-BPS branes and continuous symmetries, J. High Energy Phys. 02 (2025) 066.
  42. Dmitriy Belov and Gregory W. Moore, Holographic action for the self-dual field, arXiv:hep-th/0605038.
  43. Daniel S. Freed, Gregory W. Moore, and Graeme Segal, The uncertainty of fluxes, Commun. Math. Phys. 271, 247 (2007).
  44. See also, e.g., [45, 46, 47, 48, 49] on derivation of discrete symmetry theories from 11D formulism of string theory.

  45. Jonathan J. Heckman and Luigi Tizzano, 6D fractional quantum Hall effect, J. High Energy Phys. 05 (2018) 120.
  46. Ibrahima Bah, Federico Bonetti, Ruben Minasian, and Peter Weck, Anomaly inflow methods for SCFT constructions in Type IIB, J. High Energy Phys. 02 (2021) 116.
  47. Ibrahima Bah, Federico Bonetti, and Ruben Minasian, Discrete and higher-form symmetries in SCFTs from wrapped M5-branes, J. High Energy Phys. 03 (2021) 196.
  48. Fabio Apruzzi, Federico Bonetti, Dewi S. W. Gould, and Sakura Schafer-Nameki, Aspects of categorical symmetries from branes: SymTFTs and generalized charges, SciPost Phys. 17, 025 (2024).
  49. Craig Lawrie, Xingyang Yu, and Hao Y. Zhang, Intermediate defect groups, polarization pairs, and noninvertible duality defects, Phys. Rev. D 109, 026005 (2024).
  50. Edward Witten, AdS/CFT correspondence and topological field theory, J. High Energy Phys. 12 (1998) 012.
  51. Oren Bergman and Shinji Hirano, The holography of duality in N=4 Super-Yang-Mills theory, J. High Energy Phys. 11 (2022) 069.
  52. Iñaki García Etxebarria, Jesús Huertas, and Angel M. Uranga, SymTFT Fans: The Symmetry Theory of 4d N=4 Super Yang-Mills on spaces with boundaries, J. High Energy Phys. 03 (2025) 179.
  53. Ofer Aharony, Oren Bergman, Daniel Louis Jafferis, and Juan Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, J. High Energy Phys. 10 (2008) 091.
  54. Ofer Aharony, Oren Bergman, and Daniel Louis Jafferis, Fractional M2-branes, J. High Energy Phys. 11 (2008) 043.
  55. Marieke van Beest, Dewi S. W. Gould, Sakura Schafer-Nameki, and Yi-Nan Wang, Symmetry TFTs for 3d QFTs from M-theory, J. High Energy Phys. 02 (2023) 226.
  56. Clay Córdova, Thomas T. Dumitrescu, and Kenneth Intriligator, Exploring 2-group global symmetries, J. High Energy Phys. 02 (2019) 184.
  57. Nathan Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett. B 388, 753 (1996).
  58. Ethan Torres (private communication).
  59. Jonathan J. Heckman, Max Hübner, and Chitraang Murdia, On the holographic dual of a topological symmetry operator, Phys. Rev. D 110, 046007 (2024).
  60. Davide Gaiotto and Alessandro Tomasiello, The gauge dual of Romans mass, J. High Energy Phys. 01 (2010) 015.
  61. Jonathan J. Heckman, Andrew P. Turner, and Xingyang Yu, Disorder averaging and its UV discontents, Phys. Rev. D 105, 086021 (2022).
  62. F. Gagliano and I. Garcia Etxebarria, Symtfts for u(1) symmetries from descent, arXiv:2411.15126.

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