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Symmetry breaking in the self-dual higher-spin theory

V. E. Didenko1,* and I. S. Faliakhov2,†

  • *Contact author: didenko@lpi.ru
  • †Contact author: faliakhov.is@phystech.edu
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Phys. Rev. D 112, 106010 – Published 18 November, 2025

DOI: https://doi.org/10.1103/nmxv-c8kx

Abstract

We explore the symmetry-broken phase of the self-dual (chiral) sector of higher-spin theory in four dimensions. To that end, we construct a two-parameter vacuum that breaks the anti–de Sitter (AdS) symmetry but remains symmetric under the leftover Poincaré algebra in three dimensions. The vacuum nonzero fields include spin-two AdS frame fields and a scalar, which has a profile that extends along the AdS radial direction. The two free parameters correspond to two scalar branches of conformal dimensions Δ=1 and Δ=2. Focusing on the Δ=1 branch, we analyze the dynamics of free fields around this vacuum and examine its holographic dual. We observe that certain higher spin states decouple in the broken phase. This is illustrated by a set of gauge fluctuations, which acquire no source from higher-spin currents, leading to their complete decoupling, except for the gauge field associated with spin one. The dual higher-spin currents appear to be disentangled from the gauge fields and generally do not conserve; however, their lower-spin components with helicities s=−1, 0, and ±1/2 remain unaffected by the symmetry breaking. Notably, the helicity s=+1 current, while deformed, remains conserved.

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References (90)

  1. S. Weinberg, Photons and gravitons in S-matrix theory: Derivation of charge conservation and equality of gravitational and inertial mass, Phys. Rev. 135, B1049 (1964).
  2. S. R. Coleman and J. Mandula, All possible symmetries of the S matrix, Phys. Rev. 159, 1251 (1967).
  3. C. Aragone and S. Deser, Consistency problems of hypergravity, Phys. Lett. 86B, 161 (1979).
  4. M. Taronna, On the nonlocal obstruction to interacting higher spins in flat space, J. High Energy Phys. 05 (2017) 026.
  5. R. Roiban and A. A. Tseytlin, On four-point interactions in massless higher spin theory in flat space, J. High Energy Phys. 04 (2017) 139.
  6. X. Bekaert, N. Boulanger, and P. Sundell, How higher-spin gravity surpasses the spin two barrier: No-go theorems versus yes-go examples, Rev. Mod. Phys. 84, 987 (2012).
  7. E. S. Fradkin and M. A. Vasiliev, Cubic interaction in extended theories of massless higher spin fields, Nucl. Phys. B291, 141 (1987).
  8. E. S. Fradkin and M. A. Vasiliev, On the gravitational interaction of massless higher spin fields, Phys. Lett. B 189, 89 (1987).
  9. R. R. Metsaev, Poincare invariant dynamics of massless higher spins: Fourth order analysis on mass shell, Mod. Phys. Lett. A 06, 359 (1991).
  10. R. R. Metsaev, Effective action in string theory, PhD thesis, Lebedev Physical Institute, 1991.
  11. D. Ponomarev, Chiral higher spin theories and self-duality, J. High Energy Phys. 12 (2017) 141.
  12. X. Bekaert, N. Boulanger, A. Campoleoni, M. Chiodaroli, D. Francia, M. Grigoriev, E. Sezgin, and E. Skvortsov, Snowmass white paper: Higher spin gravity and higher spin symmetry, arXiv:2205.01567.
  13. I. Buchbinder, E. Ivanov, and N. Zaigraev, Unconstrained off-shell superfield formulation of 4D, N=2 supersymmetric higher spins, J. High Energy Phys. 12 (2021) 016.
  14. I. Buchbinder, E. Ivanov, and N. Zaigraev, Off-shell cubic hypermultiplet couplings to N=2 higher spin gauge superfields, J. High Energy Phys. 05 (2022) 104.
  15. Y. A. Tatarenko and M. A. Vasiliev, Bilinear Fronsdal currents in the AdS4 higher-spin theory, J. High Energy Phys. 07 (2024) 246.
  16. Y. M. Zinoviev, On the Fradkin-Vasiliev formalism in d=4, Nucl. Phys. B1012, 116839 (2025).
  17. X. Bekaert, J. Erdmenger, D. Ponomarev, and C. Sleight, Quartic AdS interactions in higher-spin gravity from conformal field theory, J. High Energy Phys. 11 (2015) 149.
  18. Y. Neiman, Quartic locality of higher-spin gravity in de Sitter and euclidean anti-de Sitter space, Phys. Lett. B 843, 138048 (2023).
  19. O. A. Gelfond, Moderately non-local ηη¯ vertices in the AdS4 higher-spin gauge theory, Eur. Phys. J. C 83, 1154 (2023).
  20. M. A. Vasiliev, More on equations of motion for interacting massless fields of all spins in (3+1)-dimensions, Phys. Lett. B 285, 225 (1992).
  21. M. A. Vasiliev, Consistent equations for interacting massless fields of all spins in the first order in curvatures, Ann. Phys. (N.Y.) 190, 59 (1989).
  22. N. Misuna, Unfolded dynamics approach and quantum field theory, J. High Energy Phys. 12 (2023) 119.
  23. N. Misuna, Scalar electrodynamics and Higgs mechanism in the unfolded dynamics approach, J. High Energy Phys. 12 (2024) 090.
  24. N. Misuna, Unfolded formulation of 4D Yang-Mills theory, Phys. Lett. B 870, 139882 (2025).
  25. C. Fronsdal, Massless fields with integer spin, Phys. Rev. D 18, 3624 (1978).
  26. M. A. Vasiliev, Higher spin gauge theories: Star product and AdS space, arXiv:hep-th/9910096.
  27. X. Bekaert, S. Cnockaert, C. Iazeolla, and M. A. Vasiliev, Nonlinear higher spin theories in various dimensions, arXiv:hep-th/0503128.
  28. V. E. Didenko and E. D. Skvortsov, Elements of Vasiliev theory, Lect. Notes Phys. 1028, 269 (2024).
  29. O. A. Gelfond and A. V. Korybut, Manifest form of the spin-local higher-spin vertex ϒωCCCηη, Eur. Phys. J. C 81, 605 (2021).
  30. S. F. Prokushkin and M. A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3-D AdS space-time, Nucl. Phys. B545, 385 (1999).
  31. S. Giombi and X. Yin, Higher spin gauge theory and holography: The three-point functions, J. High Energy Phys. 09 (2010) 115.
  32. N. Boulanger, P. Kessel, E. D. Skvortsov, and M. Taronna, Higher spin interactions in four-dimensions: Vasiliev versus fronsdal, J. Phys. A 49, 095402 (2016).
  33. M. A. Vasiliev, Current interactions and holography from the 0-form sector of nonlinear higher-spin equations, J. High Energy Phys. 10 (2017) 111.
  34. M. A. Vasiliev, Differential contracting homotopy in higher-spin theory, J. High Energy Phys. 11 (2023) 048.
  35. P. T. Kirakosiants, D. A. Valerev, and M. A. Vasiliev, Quadratic corrections to the higher-spin equations by the differential homotopy approach, arXiv:2506.16634.
  36. I. R. Klebanov and A. M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550, 213 (2002).
  37. R. G. Leigh and A. C. Petkou, Holography of the N=1 higher spin theory on AdS(4), J. High Energy Phys. 06 (2003) 011.
  38. E. Sezgin and P. Sundell, Holography in 4D (super) higher spin theories and a test via cubic scalar couplings, J. High Energy Phys. 07 (2005) 044.
  39. C. Sleight and M. Taronna, Higher-spin gauge theories and bulk locality, Phys. Rev. Lett. 121, 171604 (2018).
  40. T. Tran, Toward a twistor action for chiral higher-spin gravity, Phys. Rev. D 107, 046015 (2023).
  41. M. Tsulaia and D. Weissman, Supersymmetric quantum chiral higher spin gravity, J. High Energy Phys. 12 (2022) 002.
  42. T. Adamo and T. Tran, Higher-spin Yang–Mills, amplitudes and self-duality, Lett. Math. Phys. 113, 50 (2023).
  43. R. Monteiro, From moyal deformations to chiral higher-spin theories and to celestial algebras, J. High Energy Phys. 03 (2023) 062.
  44. D. Ponomarev, Chiral higher-spin double copy, J. High Energy Phys. 01 (2025) 143.
  45. M. Serrani, On classification of (self-dual) higher-spin gravities in flat space, J. High Energy Phys. 08 (2025) 032.
  46. A. K. H. Bengtsson, A proposal for the role of higher spin fields in conformal cyclic cosmology, arXiv:2507.06634.
  47. T. Basile, Massless chiral fields in six dimensions, SciPost Phys. 19, 079 (2025).
  48. O. A. Gelfond and M. A. Vasiliev, Homotopy operators and locality theorems in higher-spin equations, Phys. Lett. B 786, 180 (2018).
  49. V. E. Didenko, O. A. Gelfond, A. V. Korybut, and M. A. Vasiliev, Spin-locality of η2 and η¯2 quartic higher-spin vertices, J. High Energy Phys. 12 (2020) 184.
  50. V. E. Didenko, O. A. Gelfond, A. V. Korybut, and M. A. Vasiliev, Homotopy properties and lower-order vertices in higher-spin equations, J. Phys. A 51, 465202 (2018).
  51. O. A. Gelfond and M. A. Vasiliev, Spin-locality of higher-spin theories and star-product functional classes, J. High Energy Phys. 03 (2020) 002.
  52. V. E. Didenko, O. A. Gelfond, A. V. Korybut, and M. A. Vasiliev, Limiting shifted homotopy in higher-spin theory and spin-locality, J. High Energy Phys. 12 (2019) 086.
  53. V. E. Didenko and A. V. Korybut, On z-dominance, shift symmetry and spin locality in higher-spin theory, J. High Energy Phys. 05 (2023) 133.
  54. V. E. Didenko, On holomorphic sector of higher-spin theory, J. High Energy Phys. 10 (2022) 191.
  55. V. E. Didenko and M. A. Povarnin, All vertices for unconstrained symmetric gauge fields, Phys. Rev. D 110, 126012 (2024); 111, 109901(E) (2025).
  56. A. Sharapov, E. Skvortsov, A. Sukhanov, and R. Van Dongen, More on chiral higher spin gravity and convex geometry, Nucl. Phys. B990, 116152 (2023).
  57. M. A. Vasiliev, Projectively-compact spinor vertices and space-time spin-locality in higher-spin theory, Phys. Lett. B 834, 137401 (2022).
  58. D. J. Gross and P. F. Mende, The high-energy behavior of string scattering amplitudes, Phys. Lett. B 197, 129 (1987).
  59. D. J. Gross and P. F. Mende, String theory beyond the Planck scale, Nucl. Phys. B303, 407 (1988).
  60. D. J. Gross, High-energy symmetries of string theory, Phys. Rev. Lett. 60, 1229 (1988).
  61. B. Sundborg, Stringy gravity, interacting tensionless strings and massless higher spins, Nucl. Phys. B, Proc. Suppl. 102, 113 (2001).
  62. E. Sezgin and P. Sundell, Massless higher spins and holography, Nucl. Phys. B644, 303 (2002); B660, 403(E) (2003).
  63. G. Bonelli, On the tensionless limit of bosonic strings, infinite symmetries and higher spins, Nucl. Phys. B669, 159 (2003).
  64. A. Sagnotti and M. Tsulaia, On higher spins and the tensionless limit of string theory, Nucl. Phys. B682, 83 (2004).
  65. A. Sagnotti, Notes on strings and higher spins, J. Phys. A 46, 214006 (2013).
  66. M. A. Vasiliev, From coxeter higher-spin theories to strings and tensor models, J. High Energy Phys. 08 (2018) 051.
  67. A. A. Tarusov, K. A. Ushakov, and M. A. Vasiliev, Linearized coxeter higher-spin theories, J. High Energy Phys. 08 (2025) 052.
  68. R. R. Metsaev, IIB supergravity and various aspects of light cone formalism in AdS space-time, arXiv:hep-th/0002008.
  69. C. Y. R. Chen, E. Joung, K. Mkrtchyan, and J. Yoon, Higher-order chiral scalar from boundary reduction of 3D higher-spin gravity, J. High Energy Phys. 05 (2025) 186.
  70. M. R. Gaberdiel and R. Gopakumar, Tensionless string spectra on AdS3, J. High Energy Phys. 05 (2018) 085.
  71. L. Eberhardt, M. R. Gaberdiel, and R. Gopakumar, The worldsheet dual of the symmetric product CFT, J. High Energy Phys. 04 (2019) 103.
  72. L. Eberhardt, M. R. Gaberdiel, and R. Gopakumar, Deriving the AdS3/CFT2 correspondence, J. High Energy Phys. 02 (2020) 136.
  73. V. E. Didenko and A. V. Korybut, Interaction of symmetric higher-spin gauge fields, Phys. Rev. D 108, 086031 (2023); 109, 069901(E) (2024).
  74. V. E. Didenko and A. V. Korybut, Toward higher-spin symmetry breaking in the bulk, Phys. Rev. D 110, 026007 (2024).
  75. R. Aros, C. Iazeolla, J. Noreña, E. Sezgin, P. Sundell, and Y. Yin, FRW and domain walls in higher spin gravity, J. High Energy Phys. 03 (2018) 153.
  76. M. Flato and C. Fronsdal, One massless particle equals two Dirac singletons: Elementary particles in a curved space. 6., Lett. Math. Phys. 2, 421 (1978).
  77. M. A. Vasiliev, Holography, unfolding and higher-spin theory, J. Phys. A 46, 214013 (2013).
  78. F. Diaz, C. Iazeolla, and P. Sundell, Fractional spins, unfolding, and holography. Part I. Parent field equations for dual higher-spin gravity reductions, J. High Energy Phys. 09 (2024) 109.
  79. F. Diaz, C. Iazeolla, and P. Sundell, Fractional spins, unfolding, and holography. Part II. 4D higher spin gravity and 3D conformal dual, J. High Energy Phys. 10 (2024) 066.
  80. A. V. Korybut, On consistency of the interacting (anti)holomorphic higher-spin sector, Eur. Phys. J. C 85, 885 (2025).
  81. V. E. Didenko and M. A. Vasiliev, Static BPS black hole in 4D higher-spin gauge theory, Phys. Lett. B 682, 305 (2009); 722, 389(E) (2013).
  82. C. Iazeolla and P. Sundell, Families of exact solutions to Vasiliev’s 4D equations with spherical, cylindrical and biaxial symmetry, J. High Energy Phys. 12 (2011) 084.
  83. P. Kraus and E. Perlmutter, Probing higher spin black holes, J. High Energy Phys. 02 (2013) 096.
  84. V. E. Didenko and A. V. Korybut, Planar solutions of higher-spin theory. Nonlinear corrections, J. High Energy Phys. 01 (2022) 125.
  85. C. Iazeolla, E. Sezgin, and P. Sundell, Real forms of complex higher spin field equations and new exact solutions, Nucl. Phys. B791, 231 (2008).
  86. V. E. Didenko and E. D. Skvortsov, Towards higher-spin holography in ambient space of any dimension, J. Phys. A 46, 214010 (2013).
  87. V. E. Didenko and E. D. Skvortsov, Exact higher-spin symmetry in CFT: All correlators in unbroken vasiliev theory, J. High Energy Phys. 04 (2013) 158.
  88. V. E. Didenko and M. A. Vasiliev, Test of the local form of higher-spin equations via AdS/CFT, Phys. Lett. B 775, 352 (2017).
  89. A. David and Y. Neiman, Bulk interactions and boundary dual of higher-spin-charged particles, J. High Energy Phys. 03 (2021) 264.
  90. V. Lysov and Y. Neiman, Higher-spin gravity’s “string”: New gauge and proof of holographic duality for the linearized Didenko-Vasiliev solution, J. High Energy Phys. 10 (2022) 054.

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Phys. Rev. D 112, 106010– Published 18 November, 2025
  • Received 8 September 2025
  • Accepted 29 October 2025
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