Papers
Topics
Authors
Recent
Search
2000 character limit reached

Low spin solutions of Higher Spin Gravity: BPST instanton

Published 25 Mar 2024 in hep-th | (2403.17148v2)

Abstract: Higher spin gravities do not have a low energy limit where higher-spin fields decouple from gravity. Nevertheless, it is possible to construct fine-tuned exact solutions that activate low-spin fields without sourcing the higher-spin fields. We show that BPST (Belavin-Polyakov-Schwartz-Tyupkin) instanton is an exact solution of Chiral Higher Spin Gravity, i.e. it is also a solution of the holographic dual of Chern-Simons matter theories. This gives an example of a low-spin solution. The instanton sources the opposite helicity spin-one field and a scalar field. We derive an Effective Field Theory that describes the coupling between an instanton and the other two fields, whose action starts with the Chalmers-Siegel action and has certain higher derivative couplings.

Authors (2)
Definition Search Book Streamline Icon: https://streamlinehq.com
References (81)
  1. 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 [hep-th].
  2. M. Blencowe, “A Consistent Interacting Massless Higher Spin Field Theory in D𝐷Ditalic_D = (2+1),” Class.Quant.Grav. 6 (1989) 443.
  3. E. Bergshoeff, M. P. Blencowe, and K. S. Stelle, “Area Preserving Diffeomorphisms and Higher Spin Algebra,” Commun. Math. Phys. 128 (1990) 213.
  4. A. Campoleoni, S. Fredenhagen, S. Pfenninger, and S. Theisen, “Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields,” JHEP 1011 (2010) 007, arXiv:1008.4744 [hep-th].
  5. M. Henneaux and S.-J. Rey, “Nonlinear W∞subscript𝑊W_{\infty}italic_W start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity,” JHEP 1012 (2010) 007, arXiv:1008.4579 [hep-th].
  6. C. N. Pope and P. K. Townsend, “Conformal Higher Spin in (2+1)-dimensions,” Phys. Lett. B225 (1989) 245–250.
  7. E. S. Fradkin and V. Ya. Linetsky, “A Superconformal Theory of Massless Higher Spin Fields in D𝐷Ditalic_D = (2+1),” Mod. Phys. Lett. A4 (1989) 731. [Annals Phys.198,293(1990)].
  8. M. Grigoriev, I. Lovrekovic, and E. Skvortsov, “New Conformal Higher Spin Gravities in 3⁢d3𝑑3d3 italic_d,” JHEP 01 (2020) 059, arXiv:1909.13305 [hep-th].
  9. M. Grigoriev, K. Mkrtchyan, and E. Skvortsov, “Matter-free higher spin gravities in 3D: Partially-massless fields and general structure,” Phys. Rev. D 102 no. 6, (2020) 066003, arXiv:2005.05931 [hep-th].
  10. A. Y. Segal, “Conformal higher spin theory,” Nucl. Phys. B664 (2003) 59–130, arXiv:hep-th/0207212 [hep-th].
  11. A. A. Tseytlin, “On limits of superstring in A⁢d⁢S5×S5𝐴𝑑subscript𝑆5superscript𝑆5AdS_{5}\times S^{5}italic_A italic_d italic_S start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT × italic_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT,” Theor. Math. Phys. 133 (2002) 1376–1389, arXiv:hep-th/0201112 [hep-th]. [Teor. Mat. Fiz.133,69(2002)].
  12. X. Bekaert, E. Joung, and J. Mourad, “Effective action in a higher-spin background,” JHEP 02 (2011) 048, arXiv:1012.2103 [hep-th].
  13. T. Basile, M. Grigoriev, and E. Skvortsov, “Covariant action for conformal higher spin gravity,” J. Phys. A 56 no. 38, (2023) 385402, arXiv:2212.10336 [hep-th].
  14. R. R. Metsaev, “Poincare invariant dynamics of massless higher spins: Fourth order analysis on mass shell,” Mod. Phys. Lett. A6 (1991) 359–367.
  15. R. R. Metsaev, “S𝑆Sitalic_S matrix approach to massless higher spins theory. 2: The Case of internal symmetry,” Mod. Phys. Lett. A6 (1991) 2411–2421.
  16. D. Ponomarev and E. D. Skvortsov, “Light-Front Higher-Spin Theories in Flat Space,” J. Phys. A50 no. 9, (2017) 095401, arXiv:1609.04655 [hep-th].
  17. E. D. Skvortsov, T. Tran, and M. Tsulaia, “Quantum Chiral Higher Spin Gravity,” Phys. Rev. Lett. 121 no. 3, (2018) 031601, arXiv:1805.00048 [hep-th].
  18. E. Skvortsov, T. Tran, and M. Tsulaia, “More on Quantum Chiral Higher Spin Gravity,” Phys. Rev. D101 no. 10, (2020) 106001, arXiv:2002.08487 [hep-th].
  19. M. Sperling and H. C. Steinacker, “Covariant 4-dimensional fuzzy spheres, matrix models and higher spin,” J. Phys. A50 no. 37, (2017) 375202, arXiv:1704.02863 [hep-th].
  20. H. Steinacker and T. Tran, “A Twistorial Description of the IKKT-Matrix Model,” arXiv:2203.05436 [hep-th].
  21. H. C. Steinacker and T. Tran, “Soft limit of higher-spin interactions in the IKKT model,” arXiv:2311.14163 [hep-th].
  22. M. Ammon, M. Gutperle, P. Kraus, and E. Perlmutter, “Spacetime Geometry in Higher Spin Gravity,” JHEP 10 (2011) 053, arXiv:1106.4788 [hep-th].
  23. M. Gutperle and P. Kraus, “Higher Spin Black Holes,” JHEP 05 (2011) 022, arXiv:1103.4304 [hep-th].
  24. M. Ammon, M. Gutperle, P. Kraus, and E. Perlmutter, “Black holes in three dimensional higher spin gravity: A review,” J. Phys. A 46 (2013) 214001, arXiv:1208.5182 [hep-th].
  25. C. Bunster, M. Henneaux, A. Perez, D. Tempo, and R. Troncoso, “Generalized Black Holes in Three-dimensional Spacetime,” JHEP 05 (2014) 031, arXiv:1404.3305 [hep-th].
  26. M. Sperling and H. C. Steinacker, “Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model,” JHEP 07 (2019) 010, arXiv:1901.03522 [hep-th].
  27. Y. Asano and H. C. Steinacker, “Spherically symmetric solutions of higher-spin gravity in the IKKT matrix model,” Nucl. Phys. B 980 (2022) 115843, arXiv:2112.08204 [hep-th].
  28. S. Fredenhagen and H. C. Steinacker, “Exploring the gravity sector of emergent higher-spin gravity: effective action and a solution,” JHEP 05 (2021) 183, arXiv:2101.07297 [hep-th].
  29. E. Sezgin and P. Sundell, “An Exact solution of 4-D higher-spin gauge theory,” Nucl.Phys. B762 (2007) 1–37, arXiv:hep-th/0508158 [hep-th].
  30. A. Sharapov and E. Skvortsov, “Characteristic Cohomology and Observables in Higher Spin Gravity,” JHEP 12 (2020) 190, arXiv:2006.13986 [hep-th].
  31. A. Sharapov and E. Skvortsov, “Chiral higher spin gravity in (A)dS4 and secrets of Chern–Simons matter theories,” Nucl. Phys. B 985 (2022) 115982, arXiv:2205.15293 [hep-th].
  32. D. Ponomarev, “Chiral Higher Spin Theories and Self-Duality,” JHEP 12 (2017) 141, arXiv:1710.00270 [hep-th].
  33. T. Tran, “Twistor constructions for higher-spin extensions of (self-dual) Yang-Mills,” JHEP 11 (2021) 117, arXiv:2107.04500 [hep-th].
  34. T. Tran, “Toward a twistor action for chiral higher-spin gravity,” Phys. Rev. D 107 no. 4, (2023) 046015, arXiv:2209.00925 [hep-th].
  35. Y. Herfray, K. Krasnov, and E. Skvortsov, “Higher-spin self-dual Yang-Mills and gravity from the twistor space,” JHEP 01 (2023) 158, arXiv:2210.06209 [hep-th].
  36. A. A. Belavin, A. M. Polyakov, A. S. Schwartz, and Y. S. Tyupkin, “Pseudoparticle Solutions of the Yang-Mills Equations,” Phys. Lett. B 59 (1975) 85–87.
  37. G. Chalmers and W. Siegel, “The Selfdual sector of QCD amplitudes,” Phys. Rev. D54 (1996) 7628–7633, arXiv:hep-th/9606061 [hep-th].
  38. M. F. Atiyah, N. J. Hitchin, V. G. Drinfeld, and Y. I. Manin, “Construction of Instantons,” Phys. Lett. A 65 (1978) 185–187.
  39. D. Sullivan, “Infinitesimal computations in topology,” Publ. Math. IHES 47 (1977) 269–331.
  40. P. van Nieuwenhuizen, “Free graded differential superalgebras,” in Group Theoretical Methods in Physics. Proceedings, 11th International Colloquium, Istanbul, Turkey, August 23-28, 1982, pp. 228–247. 1982.
  41. R. D’Auria, P. Fre, and T. Regge, “Graded Lie Algebra Cohomology and Supergravity,” Riv. Nuovo Cim. 3N12 (1980) 1.
  42. M. A. Vasiliev, “‘Gauge’ form of description of massless fields with arbitrary spin,” Sov. J. Nucl. Phys. 32 (1980) 439.
  43. M. Alexandrov, M. Kontsevich, A. Schwarz, and O. Zaboronsky, “The Geometry of the Master Equation and Topological Quantum Field Theory,” Int. J. Mod. Phys. A12 (1997) 1405–1429, arXiv:hep-th/9502010 [hep-th].
  44. G. Barnich and M. Grigoriev, “First order parent formulation for generic gauge field theories,” JHEP 1101 (2011) 122, arXiv:1009.0190 [hep-th].
  45. M. Grigoriev, “Parent formulations, frame-like Lagrangians, and generalized auxiliary fields,” JHEP 12 (2012) 048, arXiv:1204.1793 [hep-th].
  46. E. Skvortsov and R. Van Dongen, “Minimal models of field theories: SDYM and SDGR,” JHEP 08 (2022) 083, arXiv:2204.09313 [hep-th].
  47. N. Misuna, “Unfolded dynamics approach and quantum field theory,” JHEP 12 (2023) 119, arXiv:2208.04306 [hep-th].
  48. N. Misuna, “Scalar Electrodynamics and Higgs Mechanism in the Unfolded Dynamics Approach,” arXiv:2402.14164 [hep-th].
  49. R. Penrose, “Zero rest mass fields including gravitation: Asymptotic behavior,” Proc. Roy. Soc. Lond. A284 (1965) 159.
  50. N. J. Hitchin, “Linear field equations on selfdual spaces,” Proc. Roy. Soc. Lond. A370 (1980) 173–191.
  51. K. Krasnov, E. Skvortsov, and T. Tran, “Actions for Self-dual Higher Spin Gravities,” arXiv:2105.12782 [hep-th].
  52. M. A. Vasiliev, “Free massless fields of arbitrary spin in the de sitter space and initial data for a higher spin superalgebra,” Fortsch. Phys. 35 (1987) 741–770.
  53. E. Skvortsov and R. Van Dongen, “Minimal models of field theories: Chiral Higher Spin Gravity,” arXiv:2204.10285 [hep-th].
  54. R. R. Metsaev, “Cubic interaction vertices for N=1 arbitrary spin massless supermultiplets in flat space,” JHEP 08 (2019) 130, arXiv:1905.11357 [hep-th].
  55. R. R. Metsaev, “Cubic interactions for arbitrary spin 𝒩𝒩\mathcal{N}caligraphic_N -extended massless supermultiplets in 4d flat space,” JHEP 11 (2019) 084, arXiv:1909.05241 [hep-th].
  56. M. Tsulaia and D. Weissman, “Supersymmetric quantum chiral higher spin gravity,” JHEP 12 (2022) 002, arXiv:2209.13907 [hep-th].
  57. K. Krasnov, “Self-Dual Gravity,” Class. Quant. Grav. 34 no. 9, (2017) 095001, arXiv:1610.01457 [hep-th].
  58. N. Boulanger, T. Damour, L. Gualtieri, and M. Henneaux, “Inconsistency of interacting, multigraviton theories,” Nucl. Phys. B597 (2001) 127–171, arXiv:hep-th/0007220.
  59. F. Wilczek, “Inequivalent Embeddings of SU(2) and Instanton Interactions,” Phys. Lett. B 65 (1976) 160–162.
  60. A. Sharapov and E. Skvortsov, “Formal Higher Spin Gravities,” Nucl. Phys. B941 (2019) 838–860, arXiv:1901.01426 [hep-th].
  61. M. A. Vasiliev, “Closed equations for interacting gauge fields of all spins,” JETP Lett. 51 (1990) 503–507.
  62. X. Bekaert, J. Erdmenger, D. Ponomarev, and C. Sleight, “Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory,” JHEP 11 (2015) 149, arXiv:1508.04292 [hep-th].
  63. J. Maldacena, D. Simmons-Duffin, and A. Zhiboedov, “Looking for a bulk point,” JHEP 01 (2017) 013, arXiv:1509.03612 [hep-th].
  64. C. Sleight and M. Taronna, “Higher-Spin Gauge Theories and Bulk Locality,” Phys. Rev. Lett. 121 no. 17, (2018) 171604, arXiv:1704.07859 [hep-th].
  65. D. Ponomarev, “A Note on (Non)-Locality in Holographic Higher Spin Theories,” Universe 4 no. 1, (2018) 2, arXiv:1710.00403 [hep-th].
  66. Y. Neiman, “Quartic locality of higher-spin gravity in de Sitter and Euclidean anti-de Sitter space,” Phys. Lett. B 843 (2023) 138048, arXiv:2302.00852 [hep-th].
  67. S. Jain and D. K. S, “A Spin on the Bulk Locality of Slightly Broken Higher Spin Theories,” arXiv:2308.04490 [hep-th].
  68. V. E. Didenko and M. A. Vasiliev, “Static BPS black hole in 4d higher-spin gauge theory,” Phys. Lett. B 682 (2009) 305–315, arXiv:0906.3898 [hep-th]. [Erratum: Phys.Lett.B 722, 389 (2013)].
  69. C. Iazeolla and P. Sundell, “Families of exact solutions to Vasiliev’s 4D equations with spherical, cylindrical and biaxial symmetry,” JHEP 12 (2011) 084, arXiv:1107.1217 [hep-th].
  70. C. Iazeolla, E. Sezgin, and P. Sundell, “On Exact Solutions and Perturbative Schemes in Higher Spin Theory,” Universe 4 no. 1, (2018) 5, arXiv:1711.03550 [hep-th].
  71. N. Boulanger, P. Kessel, E. D. Skvortsov, and M. Taronna, “Higher spin interactions in four-dimensions: Vasiliev versus Fronsdal,” J. Phys. A49 no. 9, (2016) 095402, arXiv:1508.04139 [hep-th].
  72. V. E. Didenko and A. V. Korybut, “Planar solutions of higher-spin theory. Nonlinear corrections,” JHEP 01 (2022) 125, arXiv:2110.02256 [hep-th].
  73. C. Iazeolla, E. Sezgin, and P. Sundell, “Real forms of complex higher spin field equations and new exact solutions,” Nucl. Phys. B791 (2008) 231–264, arXiv:0706.2983 [hep-th].
  74. R. Aros, C. Iazeolla, P. Sundell, and Y. Yin, “Higher spin fluctuations on spinless 4D BTZ black hole,” JHEP 08 (2019) 171, arXiv:1903.01399 [hep-th].
  75. A. Lipstein and S. Nagy, “Self-Dual Gravity and Color-Kinematics Duality in AdS4,” Phys. Rev. Lett. 131 no. 8, (2023) 081501, arXiv:2304.07141 [hep-th].
  76. Y. Neiman, “Self-dual gravity in de Sitter space: Light-cone ansatz and static-patch scattering,” Phys. Rev. D 109 no. 2, (2024) 024039, arXiv:2303.17866 [gr-qc].
  77. R. Monteiro, “From Moyal deformations to chiral higher-spin theories and to celestial algebras,” JHEP 03 (2023) 062, arXiv:2212.11266 [hep-th].
  78. L. Ren, M. Spradlin, A. Yelleshpur Srikant, and A. Volovich, “On effective field theories with celestial duals,” JHEP 08 (2022) 251, arXiv:2206.08322 [hep-th].
  79. D. Ponomarev, “Invariant traces of the flat space chiral higher-spin algebra as scattering amplitudes,” JHEP 09 (2022) 086, arXiv:2205.09654 [hep-th].
  80. D. Ponomarev, “Towards higher-spin holography in flat space,” JHEP 01 (2023) 084, arXiv:2210.04035 [hep-th].
  81. D. Ponomarev, “Chiral higher-spin holography in flat space: the Flato-Fronsdal theorem and lower-point functions,” JHEP 01 (2023) 048, arXiv:2210.04036 [hep-th].
Citations (1)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 2 tweets with 0 likes about this paper.

Sign Up for Free