On BF-type higher-spin actions in two dimensions

Abstract

We propose a non-abelian higher-spin theory in two dimensions for an infinite multiplet of massive scalar fields and infinitely many topological higher-spin gauge fields together with their dilaton-like partners. The spectrum includes local degrees of freedom although the field equations take the form of flatness and covariant constancy conditions because fields take values in a suitable extension of the infinite-dimensional higher-spin algebra đ”„đ”°[λ]. The corresponding action functional is of BF-type and generalizes the known topological higher-spin Jackiw-Teitelboim gravity.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    D. Sorokin, Introduction to the classical theory of higher spins, AIP Conf. Proc. 767 (2005) 172 [hep-th/0405069] [INSPIRE].

  2. [2]

    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 (2012) 987 [arXiv:1007.0435] [INSPIRE].

  3. [3]

    E.S. Fradkin and M.A. Vasiliev, On the gravitational interaction of massless higher spin fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].

  4. [4]

    E.S. Fradkin and M.A. Vasiliev, Cubic interaction in extended theories of massless higher spin fields, Nucl. Phys. B 291 (1987) 141 [INSPIRE].

  5. [5]

    A.A. Tseytlin, On limits of superstring in AdS5 × S5 , Theor. Math. Phys. 133 (2002) 1376 [hep-th/0201112] [INSPIRE].

  6. [6]

    A.Y. Segal, Conformal higher spin theory, Nucl. Phys. B 664 (2003) 59 [hep-th/0207212] [INSPIRE].

  7. [7]

    X. Bekaert, E. Joung and J. Mourad, Effective action in a higher-spin background, JHEP 02 (2011) 048 [arXiv:1012.2103] [INSPIRE].

  8. [8]

    M.A. Vasiliev, More on equations of motion for interacting massless fields of all spins in (3 + 1)-dimensions, Phys. Lett. B 285 (1992) 225 [INSPIRE].

  9. [9]

    M.A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dSd , Phys. Lett. B 567 (2003) 139 [hep-th/0304049] [INSPIRE].

  10. [10]

    N. Boulanger and P. Sundell, An action principle for Vasiliev’s four-dimensional higher-spin gravity, J. Phys. A 44 (2011) 495402 [arXiv:1102.2219] [INSPIRE].

  11. [11]

    N. Boulanger, E. Sezgin and P. Sundell, 4D higher spin gravity with dynamical two-form as a Frobenius-Chern-Simons gauge theory, arXiv:1505.04957 [INSPIRE].

  12. [12]

    C. Arias et al., Action principles for higher and fractional spin gravities, in Proceedings, International Workshop on Higher Spin Gauge Theories, Singapore, 4–6 November 2015, World Scientific, Singapore (2017), pg. 213 [arXiv:1603.04454] [INSPIRE].

  13. [13]

    D. Ponomarev and E.D. Skvortsov, Light-front higher-spin theories in flat space, J. Phys. A 50 (2017) 095401 [arXiv:1609.04655] [INSPIRE].

  14. [14]

    E.D. Skvortsov, T. Tran and M. Tsulaia, Quantum chiral higher spin gravity, Phys. Rev. Lett. 121 (2018) 031601 [arXiv:1805.00048] [INSPIRE].

  15. [15]

    E. Skvortsov, Light-front bootstrap for Chern-Simons matter theories, JHEP 06 (2019) 058 [arXiv:1811.12333] [INSPIRE].

  16. [16]

    A. Achucarro and P.K. Townsend, A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories, Phys. Lett. B 180 (1986) 89 [INSPIRE].

  17. [17]

    E. Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B 311 (1988) 46 [INSPIRE].

  18. [18]

    J.H. Horne and E. Witten, Conformal gravity in three-dimensions as a gauge theory, Phys. Rev. Lett. 62 (1989) 501 [INSPIRE].

  19. [19]

    M.P. Blencowe, A consistent interacting massless higher spin field theory in D = (2 + 1), Class. Quant. Grav. 6 (1989) 443 [INSPIRE].

  20. [20]

    A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, JHEP 11 (2010) 007 [arXiv:1008.4744] [INSPIRE].

  21. [21]

    E.S. Fradkin and V. Ya. Linetsky, Conformal superalgebras of higher spins, Annals Phys. 198 (1990) 252 [INSPIRE].

  22. [22]

    M. Grigoriev, I. Lovrekovic and E. Skvortsov, New conformal higher spin gravities in 3d, JHEP 01 (2020) 059 [arXiv:1909.13305] [INSPIRE].

  23. [23]

    C. Teitelboim, Gravitation and Hamiltonian structure in two space-time dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].

  24. [24]

    R. Jackiw, Lower dimensional gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].

  25. [25]

    T. Fukuyama and K. Kamimura, Gauge theory of two-dimensional gravity, Phys. Lett. B 160 (1985) 259 [INSPIRE].

  26. [26]

    K.B. Alkalaev, On higher spin extension of the Jackiw-Teitelboim gravity model, J. Phys. A 47 (2014) 365401 [arXiv:1311.5119] [INSPIRE].

  27. [27]

    D. Grumiller, M. Leston and D. Vassilevich, Anti-de Sitter holography for gravity and higher spin theories in two dimensions, Phys. Rev. D 89 (2014) 044001 [arXiv:1311.7413] [INSPIRE].

  28. [28]

    K.B. Alkalaev, Global and local properties of AdS2 higher spin gravity, JHEP 10 (2014) 122 [arXiv:1404.5330] [INSPIRE].

  29. [29]

    E.S. Fradkin and V. Ya. Linetsky, Higher spin symmetry in one-dimension and two-dimensions. 1, Mod. Phys. Lett. A 4 (1989) 2635 [INSPIRE].

  30. [30]

    E.S. Fradkin and V. Ya. Linetsky, Higher spin symmetry in one-dimension and two-dimensions. 2, Mod. Phys. Lett. A 4 (1989) 2649 [INSPIRE].

  31. [31]

    B.L. Feigin, Lie algebras gl(λ) and cohomologies of Lie algebras of differential operators, Russ. Math. Surv. 43 (1988) 169.

  32. [32]

    M.A. Vasiliev, Higher spin algebras and quantization on the sphere and hyperboloid, Int. J. Mod. Phys. A 6 (1991) 1115 [INSPIRE].

  33. [33]

    K. Alkalaev and X. Bekaert, Towards higher-spin AdS2 /CFT1 holography, JHEP 04 (2020) 206 [arXiv:1911.13212] [INSPIRE].

  34. [34]

    P. Kessel and K. Mkrtchyan, Cubic interactions of massless bosonic fields in three dimensions II: parity-odd and Chern-Simons vertices, Phys. Rev. D 97 (2018) 106021 [arXiv:1803.02737] [INSPIRE].

  35. [35]

    X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, in Higher spin gauge theories: proceedings, 1st Solvay Workshop, Brussels, Belgium, 12–14 May 2004, pg. 132 [hep-th/0503128] [INSPIRE].

  36. [36]

    E.D. Skvortsov and M.A. Vasiliev, Geometric formulation for partially massless fields, Nucl. Phys. B 756 (2006) 117 [hep-th/0601095] [INSPIRE].

  37. [37]

    V.E. Lopatin and M.A. Vasiliev, Free massless bosonic fields of arbitrary spin in d-dimensional de Sitter space, Mod. Phys. Lett. A 3 (1988) 257 [INSPIRE].

  38. [38]

    S. Deser and A. Waldron, Partial masslessness of higher spins in (A)dS, Nucl. Phys. B 607 (2001) 577 [hep-th/0103198] [INSPIRE].

  39. [39]

    Yu. M. Zinoviev, On massive high spin particles in AdS, hep-th/0108192 [INSPIRE].

  40. [40]

    D. Grumiller, W. Kummer and D.V. Vassilevich, Dilaton gravity in two-dimensions, Phys. Rept. 369 (2002) 327 [hep-th/0204253] [INSPIRE].

  41. [41]

    M.A. Vasiliev, Higher spin gauge interactions for matter fields in two-dimensions, Phys. Lett. B 363 (1995) 51 [hep-th/9511063] [INSPIRE].

  42. [42]

    M. Hazewinkel, N. Gubareni and V.V. Kirichenko, Algebras, rings, and modules: Lie algebras and Hopf algebras, American Mathematical Society, Providence, RI, U.S.A. (2010).

  43. [43]

    M.A. Vasiliev, Extended higher spin superalgebras and their realizations in terms of quantum operators, Fortsch. Phys. 36 (1988) 33 [INSPIRE].

  44. [44]

    S.F. Prokushkin and M.A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3D AdS space-time, Nucl. Phys. B 545 (1999) 385 [hep-th/9806236] [INSPIRE].

  45. [45]

    A. Sharapov and E. Skvortsov, A∞ algebras from slightly broken higher spin symmetries, JHEP 09 (2019) 024 [arXiv:1809.10027] [INSPIRE].

  46. [46]

    A. Sharapov and E. Skvortsov, Formal higher spin gravities, Nucl. Phys. B 941 (2019) 838 [arXiv:1901.01426] [INSPIRE].

  47. [47]

    A.V. Barabanshchikov, S.F. Prokushkin and M.A. Vasiliev, Free equations for massive matter fields in (2 + 1)-dimensional anti-de Sitter space from deformed oscillator algebra, Theor. Math. Phys. 110 (1997) 295 [Teor. Mat. Fiz. 110N3 (1997) 372] [hep-th/9609034] [INSPIRE].

  48. [48]

    S.F. Prokushkin, A. Yu. Segal and M.A. Vasiliev, Coordinate free action for AdS3 higher spin matter systems, Phys. Lett. B 478 (2000) 333 [hep-th/9912280] [INSPIRE].

  49. [49]

    R. Bonezzi, N. Boulanger, E. Sezgin and P. Sundell, An action for matter coupled higher spin gravity in three dimensions, JHEP 05 (2016) 003 [arXiv:1512.02209] [INSPIRE].

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

Author information

Affiliations

Authors

Corresponding author

Correspondence to Konstantin Alkalaev.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 2002.02387

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Verify currency and authenticity via CrossMark

Cite this article

Alkalaev, K., Bekaert, X. On BF-type higher-spin actions in two dimensions. J. High Energ. Phys. 2020, 158 (2020). https://doi.org/10.1007/JHEP05(2020)158

Download citation

Keywords

  • Higher Spin Gravity
  • Higher Spin Symmetry