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From Coxeter higher-spin theories to strings and tensor models

  • M. A. Vasiliev
Open Access
Regular Article - Theoretical Physics

Abstract

A new class of higher-spin gauge theories associated with various Coxeter groups is proposed. The emphasize is on the Bp-models. The cases of B1 and its infinite graded-symmetric product symB1) correspond to the usual higher-spin theory and its multi-particle extension, respectively. The multi-particle B2-higher-spin theory is conjectured to be associated with String Theory. Bp-higher-spin models with p > 2 are anticipated to be dual to the rank-p boundary tensor sigma-models. Bp higher-spin models with p ≥ 2 possess two coupling constants responsible for higher-spin interactions in AdS background and stringy/tensor effects, respectively. The brane-like idempotent extension of the Coxeter higher-spin theory is proposed allowing to unify in the same model the fields supported by space-times of different dimensions. Consistency of the holographic interpretation of the boundary matrix-like model in the B2-higher-spin model is shown to demand N ≥ 4 SUSY, suggesting duality with the N = 4 SYM upon spontaneous breaking of higher-spin symmetries. The proposed models are shown to admit unitary truncations.

Keywords

AdS-CFT Correspondence Higher Spin Gravity Higher Spin Symmetry 

Notes

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.

References

  1. [1]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
  2. [2]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3+1)-dimensions, Phys. Lett. B 243 (1990) 378 [INSPIRE].
  5. [5]
    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].
  6. [6]
    M.A. Vasiliev, Higher spin gauge theories: star product and AdS space, hep-th/9910096 [INSPIRE].
  7. [7]
    E.S. Fradkin and M.A. Vasiliev, On the gravitational interaction of massless higher spin fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  8. [8]
    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].
  9. [9]
    S.F. Prokushkin and M.A. Vasiliev, Cohomology of arbitrary spin currents in AdS 3, Theor. Math. Phys. 123 (2000) 415 [hep-th/9907020] [INSPIRE].CrossRefzbMATHGoogle Scholar
  10. [10]
    M.A. Vasiliev, Star-product functions in higher-spin theory and locality, JHEP 06 (2015) 031 [arXiv:1502.02271] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  11. [11]
    N. Boulanger, P. Kessel, E.D. Skvortsov and M. Taronna, Higher spin interactions in four-dimensions: Vasiliev versus Fronsdal, J. Phys. A 49 (2016) 095402 [arXiv:1508.04139] [INSPIRE].
  12. [12]
    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] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  13. [13]
    E.D. Skvortsov and M. Taronna, On locality, holography and unfolding, JHEP 11 (2015) 044 [arXiv:1508.04764] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    M.A. Vasiliev, Current interactions and holography from the 0-form sector of nonlinear higher-spin equations, JHEP 10 (2017) 111 [arXiv:1605.02662] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  15. [15]
    M.A. Vasiliev, On the local frame in nonlinear higher-spin equations, JHEP 01 (2018) 062 [arXiv:1707.03735] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  16. [16]
    D. Ponomarev, A note on (non)-locality in holographic higher spin theories, Universe 4 (2018) 2 [arXiv:1710.00403] [INSPIRE].
  17. [17]
    O.A. Gelfond and M.A. Vasiliev, Homotopy operators and locality theorems in higher-spin equations, arXiv:1805.11941 [INSPIRE].
  18. [18]
    V.E. Didenko, O.A. Gelfond, A.V. Korybut and M.A. Vasiliev, Homotopy properties and lower-order vertices in higher-spin equations, arXiv:1807.00001.
  19. [19]
    M.B. Green, J.H. Schwarz and E. Witten, Superstring theory. Volume 1: introduction, Cambridge University Press, Cambridge U.K. (1987).Google Scholar
  20. [20]
    D.J. Gross and P.F. Mende, String theory beyond the Planck scale, Nucl. Phys. B 303 (1988) 407 [INSPIRE].
  21. [21]
    D.J. Gross, High-Energy Symmetries of String Theory, Phys. Rev. Lett. 60 (1988) 1229 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  22. [22]
    M.A. Vasiliev, Massless fields of all spins in the Anti-de Sitter space and their gravitational interaction, in the proceedings of the 21st International Symposium on Theory of Elementary Particles, October 12-16, Sellin, Germany (1987).Google Scholar
  23. [23]
    S.E. Konshtein and M.A. Vasiliev, Massless representations and admissibility condition for higher spin superalgebras, Nucl. Phys. B 312 (1989) 402 [INSPIRE].
  24. [24]
    R.R. Metsaev, IIB supergravity and various aspects of light cone formalism in AdS space-time, hep-th/0002008 [INSPIRE].
  25. [25]
    A. Sagnotti, Notes on strings and higher spins, J. Phys. A 46 (2013) 214006 [arXiv:1112.4285] [INSPIRE].ADSzbMATHMathSciNetGoogle Scholar
  26. [26]
    M. Bianchi, J.F. Morales and H. Samtleben, On stringy AdS 5 × S 5 and higher spin holography, JHEP 07 (2003) 062 [hep-th/0305052] [INSPIRE].
  27. [27]
    N. Beisert, M. Bianchi, J.F. Morales and H. Samtleben, Higher spin symmetry and N = 4 SYM, JHEP 07 (2004) 058 [hep-th/0405057] [INSPIRE].
  28. [28]
    M. Bianchi, Higher spin symmetry (breaking) in N = 4 SYM theory and holography, Comptes Rendus Physique 5 (2004) 1091 [hep-th/0409292] [INSPIRE].
  29. [29]
    M. Bianchi and V. Didenko, Massive higher spin multiplets and holography, hep-th/0502220 [INSPIRE].
  30. [30]
    U. Lindström and M. Zabzine, Tensionless strings, WZW models at critical level and massless higher spin fields, Phys. Lett. B 584 (2004) 178 [hep-th/0305098] [INSPIRE].
  31. [31]
    G. Bonelli, On the tensionless limit of bosonic strings, infinite symmetries and higher spins, Nucl. Phys. B 669 (2003) 159 [hep-th/0305155] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  32. [32]
    A. Sagnotti and M. Tsulaia, On higher spins and the tensionless limit of string theory, Nucl. Phys. B 682 (2004) 83 [hep-th/0311257] [INSPIRE].
  33. [33]
    J. Engquist and P. Sundell, Brane partons and singleton strings, Nucl. Phys. B 752 (2006) 206 [hep-th/0508124] [INSPIRE].
  34. [34]
    J. Engquist, P. Sundell and L. Tamassia, On singleton composites in non-compact WZW models, JHEP 02 (2007) 097 [hep-th/0701051] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  35. [35]
    S.E. Konstein, M.A. Vasiliev and V.N. Zaikin, Conformal higher spin currents in any dimension and AdS/CFT correspondence, JHEP 12 (2000) 018 [hep-th/0010239] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  36. [36]
    B. Sundborg, Stringy gravity, interacting tensionless strings and massless higher spins, Nucl. Phys. Proc. Suppl. 102 (2001) 113 [hep-th/0103247] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  37. [37]
    E. Witten, Spacetime reconstruction, talk at the John Schwarz 60thbirthday symposium, November 3-4, California Institute of Technology, U.S.A. (2001).
  38. [38]
    A. Mikhailov, Notes on higher spin symmetries, hep-th/0201019 [INSPIRE].
  39. [39]
    E. Sezgin and P. Sundell, Massless higher spins and holography, Nucl. Phys. B 644 (2002) 303 [Erratum ibid. B 660 (2003) 403] [hep-th/0205131] [INSPIRE].
  40. [40]
    M. Flato and C. Fronsdal, One massless particle equals two Dirac singletons: elementary particles in a curved space. 6., Lett. Math. Phys. 2 (1978) 421 [INSPIRE].
  41. [41]
    I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
  42. [42]
    S. Giombi and X. Yin, Higher spin gauge theory and holography: the three-point functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  43. [43]
    S. Giombi and X. Yin, Higher spins in AdS and twistorial holography, JHEP 04 (2011) 086 [arXiv:1004.3736] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  44. [44]
    J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a higher spin symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].
  45. [45]
    J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a slightly broken higher spin symmetry, Class. Quant. Grav. 30 (2013) 104003 [arXiv:1204.3882] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  46. [46]
    O. Aharony, G. Gur-Ari and R. Yacoby, d = 3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories, JHEP 03 (2012) 037 [arXiv:1110.4382] [INSPIRE].
  47. [47]
    R.G. Leigh and A.C. Petkou, Holography of the N = 1 higher spin theory on AdS 4, JHEP 06 (2003) 011 [hep-th/0304217] [INSPIRE].
  48. [48]
    E. Sezgin and P. Sundell, Holography in 4D (super) higher spin theories and a test via cubic scalar couplings, JHEP 07 (2005) 044 [hep-th/0305040] [INSPIRE].
  49. [49]
    S. Giombi et al., Chern-Simons theory with vector fermion matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].
  50. [50]
    S. Giombi and X. Yin, The higher spin/vector model duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].
  51. [51]
    E. Sezgin, E.D. Skvortsov and Y. Zhu, Chern-Simons matter theories and higher spin gravity, JHEP 07 (2017) 133 [arXiv:1705.03197] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  52. [52]
    V.E. Didenko and M.A. Vasiliev, Test of the local form of higher-spin equations via AdS/CFT, Phys. Lett. B 775 (2017) 352 [arXiv:1705.03440] [INSPIRE].
  53. [53]
    S. Jain, S. Minwalla and S. Yokoyama, Chern Simons duality with a fundamental boson and fermion, JHEP 11 (2013) 037 [arXiv:1305.7235] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    G. Gur-Ari and R. Yacoby, Three dimensional bosonization from supersymmetry, JHEP 11 (2015) 013 [arXiv:1507.04378] [INSPIRE].
  55. [55]
    N. Seiberg, T. Senthil, C. Wang and E. Witten, A duality web in 2 + 1 dimensions and condensed matter physics, Annals Phys. 374 (2016) 395 [arXiv:1606.01989] [INSPIRE].
  56. [56]
    N. Misuna, On current contribution to Fronsdal equations, Phys. Lett. B 778 (2018) 71 [arXiv:1706.04605] [INSPIRE].
  57. [57]
    O.A. Gelfond and M.A. Vasiliev, Current interactions from the one-form sector of nonlinear higher-spin equations, Nucl. Phys. B 931 (2018) 383 [arXiv:1706.03718] [INSPIRE].
  58. [58]
    M.R. Gaberdiel and R. Gopakumar, An AdS 3 dual for minimal model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].
  59. [59]
    M.R. Gaberdiel and R. Gopakumar, Minimal Model Holography, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [INSPIRE].
  60. [60]
    M. Henneaux and S.-J. Rey, Nonlinear W as asymptotic symmetry of three-dimensional higher spin Anti-de Sitter gravity, JHEP 12 (2010) 007 [arXiv:1008.4579] [INSPIRE].
  61. [61]
    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].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  62. [62]
    M.R. Gaberdiel and T. Hartman, Symmetries of holographic minimal models, JHEP 05 (2011) 031 [arXiv:1101.2910] [INSPIRE].
  63. [63]
    C. Ahn, The large N ’t Hooft limit of coset minimal models, JHEP 10 (2011) 125 [arXiv:1106.0351] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  64. [64]
    M.R. Gaberdiel, R. Gopakumar, T. Hartman and S. Raju, Partition functions of holographic minimal models, JHEP 08 (2011) 077 [arXiv:1106.1897] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  65. [65]
    C.-M. Chang and X. Yin, Higher spin gravity with matter in AdS 3 and its CFT dual, JHEP 10 (2012) 024 [arXiv:1106.2580] [INSPIRE].
  66. [66]
    A. Campoleoni, S. Fredenhagen and S. Pfenninger, Asymptotic W-symmetries in three-dimensional higher-spin gauge theories, JHEP 09 (2011) 113 [arXiv:1107.0290] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  67. [67]
    P. Kraus and E. Perlmutter, Partition functions of higher spin black holes and their CFT duals, JHEP 11 (2011) 061 [arXiv:1108.2567] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  68. [68]
    M. Ammon, P. Kraus and E. Perlmutter, Scalar fields and three-point functions in D = 3 higher spin gravity, JHEP 07 (2012) 113 [arXiv:1111.3926] [INSPIRE].
  69. [69]
    M. Beccaria, C. Candu, M.R. Gaberdiel and M. Groher, N = 1 extension of minimal model holography, JHEP 07 (2013) 174 [arXiv:1305.1048] [INSPIRE].
  70. [70]
    M.R. Gaberdiel and R. Gopakumar, Higher spins & strings, JHEP 11 (2014) 044 [arXiv:1406.6103] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  71. [71]
    M.R. Gaberdiel and R. Gopakumar, Stringy symmetries and the higher spin square, J. Phys. A 48 (2015) 185402 [arXiv:1501.07236] [INSPIRE].
  72. [72]
    M.R. Gaberdiel, C. Peng and I.G. Zadeh, Higgsing the stringy higher spin symmetry, JHEP 10 (2015) 101 [arXiv:1506.02045] [INSPIRE].
  73. [73]
    M.R. Gaberdiel and R. Gopakumar, String theory as a higher spin theory, JHEP 09 (2016) 085 [arXiv:1512.07237] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  74. [74]
    M.R. Gaberdiel, R. Gopakumar, W. Li and C. Peng, Higher spins and Yangian symmetries, JHEP 04 (2017) 152 [arXiv:1702.05100] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  75. [75]
    M.R. Gaberdiel and R. Gopakumar, Tensionless string spectra on AdS 3, JHEP 05 (2018) 085 [arXiv:1803.04423] [INSPIRE].
  76. [76]
    G. Giribet et al., Superstrings on AdS3 at k = 1, arXiv:1803.04420 [INSPIRE].
  77. [77]
    I.R. Klebanov and G. Tarnopolsky, Uncolored random tensors, melon diagrams and the Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 046004 [arXiv:1611.08915] [INSPIRE].
  78. [78]
    M. Beccaria and A.A. Tseytlin, Partition function of free conformal fields in 3-plet representation, JHEP 05 (2017) 053 [arXiv:1703.04460] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  79. [79]
    I.R. Klebanov and G. Tarnopolsky, On large N limit of symmetric traceless tensor models, JHEP 10 (2017) 037 [arXiv:1706.00839] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  80. [80]
    S. Giombi, I.R. Klebanov and G. Tarnopolsky, Bosonic tensor models at large N and smal ϵ, Phys. Rev. D 96 (2017) 106014 [arXiv:1707.03866] [INSPIRE].
  81. [81]
    K. Bulycheva, I.R. Klebanov, A. Milekhin and G. Tarnopolsky, Spectra of operators in large N tensor models, Phys. Rev. D 97 (2018) 026016 [arXiv:1707.09347] [INSPIRE].
  82. [82]
    E. Witten, An SYK-like model without disorder, arXiv:1610.09758 [INSPIRE].
  83. [83]
    S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
  84. [84]
    A. Kitaev, A simple model of quantum holography, talks given at KITP, April 7 and May 27 (2015).
  85. [85]
    J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
  86. [86]
    D.J. Gross and V. Rosenhaus, A generalization of Sachdev-Ye-Kitaev, JHEP 02 (2017) 093 [arXiv:1610.01569] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  87. [87]
    D.J. Gross and V. Rosenhaus, The bulk dual of SYK: cubic couplings, JHEP 05 (2017) 092 [arXiv:1702.08016] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  88. [88]
    D.J. Gross and V. Rosenhaus, A line of CFTs: from generalized free fields to SYK, JHEP 07 (2017) 086 [arXiv:1706.07015] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  89. [89]
    D.J. Gross and V. Rosenhaus, All point correlation functions in SYK, JHEP 12 (2017) 148 [arXiv:1710.08113] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  90. [90]
    R. de Mello Koch, R. Mello Koch, D. Gossman and L. Tribelhorn, Gauge invariants, correlators and holography in bosonic and fermionic tensor models, JHEP 09 (2017) 011 [arXiv:1707.01455] [INSPIRE].CrossRefzbMATHMathSciNetGoogle Scholar
  91. [91]
    M.A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dS(d), Phys. Lett. B 567 (2003) 139 [hep-th/0304049] [INSPIRE].
  92. [92]
    M.A. Vasiliev, Holography, unfolding and higher-spin theory, J. Phys. A 46 (2013) 214013 [arXiv:1203.5554] [INSPIRE].
  93. [93]
    S. Giombi et al., AdS description of induced higher-spin gauge theory, JHEP 10 (2013) 016 [arXiv:1306.5242] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  94. [94]
    M.A. Vasiliev, Multiparticle extension of the higher-spin algebra, Class. Quant. Grav. 30 (2013) 104006 [arXiv:1212.6071] [INSPIRE].
  95. [95]
    A.P. Polychronakos, Exchange operator formalism for integrable systems of particles, Phys. Rev. Lett. 69 (1992) 703 [hep-th/9202057] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  96. [96]
    L. Brink, T.H. Hansson and M.A. Vasiliev, Explicit solution to the N body Calogero problem, Phys. Lett. B 286 (1992) 109 [hep-th/9206049] [INSPIRE].
  97. [97]
    L. Brink, T.H. Hansson, S. Konstein and M.A. Vasiliev, The Calogero model: anyonic representation, fermionic extension and supersymmetry, Nucl. Phys. B 401 (1993) 591 [hep-th/9302023] [INSPIRE].
  98. [98]
    I. Cherednik, Double affine Hecke algebras, London Mathematical Society Lecture Note Series 319, Cambridge University Press, Cambridge U.K. (2005).Google Scholar
  99. [99]
    N. Bourbaki, Elements of mathematics, Lie groups and Lie algebras. Chapters 4-6, Springer, Germany (2002).Google Scholar
  100. [100]
    M.A. Vasiliev, Higher spin algebras and quantization on the sphere and hyperboloid, Int. J. Mod. Phys. A 6 (1991) 1115 [INSPIRE].
  101. [101]
    E. Wigner, Do the equations of motion define the quantum mechanical commutation relations?, Phys. Rev. D 77 (1950) 711.Google Scholar
  102. [102]
    L.M. Yang, A note on the quantum rule of the harmonic oscillator, Phys. Rev. D 84 (1951) 788.Google Scholar
  103. [103]
    S. Deser and D.G. Boulware, Ambiguity of harmonic oscillator commutation relations, Nuovo Cim. 30 (1963) 23.zbMATHMathSciNetGoogle Scholar
  104. [104]
    N. Mukunda, E.C.G. Sudarshan, J.K. Sharma and C.L. Mehta, Representations and properties of parabose oscillator operators. I. Energy position and momentum eigenstates, J. Math. Phys. 21 (1980) 2386 [INSPIRE].
  105. [105]
    R.R. Metsaev, Cubic interaction vertices of totally symmetric and mixed symmetry massless representations of the Poincaré group in D = 6 space-time, Phys. Lett. B 309 (1993) 39 [INSPIRE].
  106. [106]
    R.R. Metsaev, Cubic interaction vertices of massive and massless higher spin fields, Nucl. Phys. B 759 (2006) 147 [hep-th/0512342] [INSPIRE].
  107. [107]
    R.R. Metsaev, Cubic interaction vertices for fermionic and bosonic arbitrary spin fields, Nucl. Phys. B 859 (2012) 13 [arXiv:0712.3526] [INSPIRE].
  108. [108]
    K. Alkalaev, FV-type action for AdS 5 mixed-symmetry fields, JHEP 03 (2011) 031 [arXiv:1011.6109] [INSPIRE].
  109. [109]
    N. Boulanger, E.D. Skvortsov and Yu.M. Zinoviev, Gravitational cubic interactions for a simple mixed-symmetry gauge field in AdS and flat backgrounds, J. Phys. A 44 (2011) 415403 [arXiv:1107.1872] [INSPIRE].
  110. [110]
    Yu. M. Zinoviev, Gravitational cubic interactions for a massive mixed symmetry gauge field, Class. Quant. Grav. 29 (2012) 015013 [arXiv:1107.3222] [INSPIRE].
  111. [111]
    R.R. Metsaev, BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields, Phys. Lett. B 720 (2013) 237 [arXiv:1205.3131] [INSPIRE].
  112. [112]
    M. Günaydin, Singleton and doubleton supermultiplets of space-time supergroups and infinite spin superalgebras, in the proceedings of the Trieste Conference “Supermembranes and Physics in 2+1 Dimensions”, July 17-21, Trieste, Italy (1989).Google Scholar
  113. [113]
    O.V. Shaynkman and M.A. Vasiliev, Higher spin conformal symmetry for matter fields in (2 + 1)-dimensions, Theor. Math. Phys. 128 (2001) 1155 [Teor. Mat. Fiz. 128 (2001) 378] [hep-th/0103208] [INSPIRE].
  114. [114]
    M.A. Vasiliev, Conformal higher spin symmetries of 4D massless supermultiplets and OSp(L, 2M ) invariant equations in generalized (super)space, Phys. Rev. D 66 (2002) 066006 [hep-th/0106149] [INSPIRE].
  115. [115]
    P.A.M. Dirac, A remarkable representation of the 3 + 2 de Sitter group, J. Math. Phys. 4 (1963) 901 [INSPIRE].
  116. [116]
    C. Fronsdal, Singletons and massless, integral spin fields on de Sitter space, Phys. Rev. D 20 (1979) 848 [INSPIRE].
  117. [117]
    M. Günaydin and N.P. Warner, Unitary supermultiplets of OSp(8/4, r) and the spectrum of the S 7 compactification of eleven-dimensional supergravity, Nucl. Phys. B 272 (1986) 99 [INSPIRE].
  118. [118]
    E. Bergshoeff, A. Salam, E. Sezgin and Y. Tanii, Singletons, higher spin massless states and the supermembrane, Phys. Lett. B 205 (1988) 237 [INSPIRE].
  119. [119]
    S. Ferrara and C. Fronsdal, Gauge fields as composite boundary excitations, Phys. Lett. B 433 (1998) 19 [hep-th/9802126] [INSPIRE].
  120. [120]
    I. Bars and M. Günaydin, Unitary representations of noncompact supergroups, Commun. Math. Phys. 91 (1983) 31 [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  121. [121]
    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].
  122. [122]
    E. Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
  123. [123]
    O.A. Gelfond and M.A. Vasiliev, Higher rank conformal fields in the Sp(2M) symmetric generalized space-time, Theor. Math. Phys. 145 (2005) 1400 [Teor. Mat. Fiz. 145 (2005) 35] [hep-th/0304020] [INSPIRE].
  124. [124]
    O.A. Gelfond and M.A. Vasiliev, Unfolded equations for current interactions of 4D massless fields as a free system in mixed dimensions, J. Exp. Theor. Phys. 120 (2015) 484 [arXiv:1012.3143] [INSPIRE].
  125. [125]
    I.A. Bandos, J. Lukierski and D.P. Sorokin, Superparticle models with tensorial central charges, Phys. Rev. D 61 (2000) 045002 [hep-th/9904109] [INSPIRE].
  126. [126]
    M.A. Vasiliev, Relativity, causality, locality, quantization and duality in the S(p)(2M) invariant generalized space-time, in Multiple facets of quantization and supersymmetry, M. Olshanetsky et al., World Scientific, Singapore (2002), hep-th/0111119 [INSPIRE].
  127. [127]
    I. Bandos et al., Dynamics of higher spin fields and tensorial space, JHEP 05 (2005) 031 [hep-th/0501113] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  128. [128]
    M.A. Vasiliev, Higher-spin theory and space-time metamorphoses, Lect. Notes Phys. 892 (2015) 227 [arXiv:1404.1948] [INSPIRE].
  129. [129]
    D. Sorokin and M. Tsulaia, Higher spin fields in hyperspace. A review, Universe 4 (2018) 7 [arXiv:1710.08244] [INSPIRE].
  130. [130]
    E. Witten, Twistor-like transform in ten-dimensions, Nucl. Phys. B 266 (1986) 245 [INSPIRE].
  131. [131]
    M.P. Blencowe, A consistent interacting massless higher spin field theory in D = (2 + 1), Class. Quant. Grav. 6 (1989) 443 [INSPIRE].
  132. [132]
    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].
  133. [133]
    M.A. Vasiliev, Cubic interactions of bosonic higher spin gauge fields in AdS 5, Nucl. Phys. B 616 (2001) 106 [Erratum ibid. B 652 (2003) 407] [hep-th/0106200] [INSPIRE].
  134. [134]
    M.A. Vasiliev, Higher spin superalgebras in any dimension and their representations, JHEP 12 (2004) 046 [hep-th/0404124] [INSPIRE].
  135. [135]
    M. Grigoriev and E.D. Skvortsov, Type-B formal higher spin gravity, JHEP 05 (2018) 138 [arXiv:1804.03196] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  136. [136]
    M.A. Vasiliev, Invariant functionals in higher-spin theory, Nucl. Phys. B 916 (2017) 219 [arXiv:1504.07289] [INSPIRE].
  137. [137]
    J.E. Paton and H.-M. Chan, Generalized veneziano model with isospin, Nucl. Phys. B 10 (1969) 516 [INSPIRE].
  138. [138]
    N. Marcus and A. Sagnotti, Group theory from quarks at the ends of strings, Phys. Lett. 188 (1987) 58 [INSPIRE].
  139. [139]
    S.E. Konstein and M.A. Vasiliev, Extended higher spin superalgebras and their massless representations, Nucl. Phys. B 331 (1990) 475 [INSPIRE].
  140. [140]
    M.A. Vasiliev, Higher spin gauge interactions for matter fields in two-dimensions, Phys. Lett. B 363 (1995) 51 [hep-th/9511063] [INSPIRE].
  141. [141]
    M.A. Vasiliev, On conformal, SL(4, ℝ) and Sp(8, R) symmetries of 4d massless fields, Nucl. Phys. B 793 (2008) 469 [arXiv:0707.1085] [INSPIRE].
  142. [142]
    M.A. Vasiliev, Consistent equations for interacting massless fields of all spins in the first order in curvatures, Annals Phys. 190 (1989) 59 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  143. [143]
    J. Maldacena, Einstein gravity from conformal gravity, arXiv:1105.5632 [INSPIRE].
  144. [144]
    O.A. Gelfond and M.A. Vasiliev, Operator algebra of free conformal currents via twistors, Nucl. Phys. B 876 (2013) 871 [arXiv:1301.3123] [INSPIRE].
  145. [145]
    S. Caron-Huot, Z. Komargodski, A. Sever and A. Zhiboedov, Strings from massive higher spins: the asymptotic uniqueness of the Veneziano amplitude, JHEP 10 (2017) 026 [arXiv:1607.04253] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  146. [146]
    A. Sever and A. Zhiboedov, On fine structure of strings: the universal correction to the Veneziano amplitude, JHEP 06 (2018) 054 [arXiv:1707.05270] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  147. [147]
    L. Girardello, M. Porrati and A. Zaffaroni, 3 − D interacting CFTs and generalized Higgs phenomenon in higher spin theories on AdS, Phys. Lett. B 561 (2003) 289 [hep-th/0212181] [INSPIRE].
  148. [148]
    V.E. Didenko and M.A. Vasiliev, Free field dynamics in the generalized AdS (super)space, J. Math. Phys. 45 (2004) 197 [hep-th/0301054] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  149. [149]
    M. Plyushchay, D. Sorokin and M. Tsulaia, Higher spins from tensorial charges and OSp(N—2n) symmetry, JHEP 04 (2003) 013 [hep-th/0301067] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  150. [150]
    S.E. Konstein and I.V. Tyutin, Ideals generated by traces or by supertraces in the algebra of symplectic reflections \( {H}_{1,{\nu}_1,{\nu}_2}\left({I}_2\left(2k + 1\right)\right) \), J. Nonlin. Math. Phys. 24 (2017) 3 [arXiv:1612.00536].
  151. [151]
    S.E. Konstein and I.V. Tyutin, Ideals generated by traces in the algebra of symplectic reflections \( {H}_{1,{\nu}_1,{\nu}_2}\left({I}_2(2m)\right) \), Theor. Math. Phys. 187 (2016) 706.Google Scholar

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© The Author(s) 2018

Authors and Affiliations

  1. 1.I.E. Tamm Department of Theoretical PhysicsLebedev Physical InstituteMoscowRussia

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