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Journal of High Energy Physics

, 2010:113 | Cite as

Half-integer higher spin fields in (A)dS from spinning particle models

  • Olindo Corradini
Article

Abstract

We make use of O(2r + 1) spinning particle models to construct linearized higher-spin curvatures in (A)dS spaces for fields of arbitrary half-integer spin propagating in a space of arbitrary (even) dimension: the field potentials, whose curvatures are computed with the present models, are spinor-tensors of mixed symmetry corresponding to Young tableaux with \( \frac{D}{2} - 1 \) rows and r columns, thus reducing to totally symmetric spinor-tensors in four dimensions. The paper generalizes similar results obtained in the context of integer spins in (A)dS.

Keywords

Gauge Symmetry Supergravity Models Sigma Models 

References

  1. [1]
    M.A. Vasiliev, Higher spin gauge theories in various dimensions, Fortsch. Phys. 52 (2004) 702 [hep-th/0401177] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  2. [2]
    D. Sorokin, Introduction to the classical theory of higher spins, AIP Conf. Proc. 767 (2005) 172 [hep-th/0405069] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    N. Bouatta, G. Compere and A. Sagnotti, An introduction to free higher-spin fields, hep-th/0409068 [SPIRES].
  4. [4]
    X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, hep-th/0503128 [SPIRES].
  5. [5]
    A. Fotopoulos and M. Tsulaia, Gauge invariant lagrangians for free and interacting higher spin fields. A review of the BRST formulation, Int. J. Mod. Phys. A 24 (2009) 1 [arXiv:0805.1346] [SPIRES].MathSciNetADSGoogle Scholar
  6. [6]
    P. Benincasa and F. Cachazo, Consistency conditions on the S-matrix of massless particles, arXiv:0705.4305 [SPIRES].
  7. [7]
    M. Porrati, Universal limits on massless high-spin particles, Phys. Rev. D 78 (2008) 065016 [arXiv:0804.4672] [SPIRES].MathSciNetADSGoogle Scholar
  8. [8]
    C. Schubert, Perturbative quantum field theory in the string-inspired formalism, Phys. Rept. 355 (2001) 73 [hep-th/0101036] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    V.D. Gershun and V.I. Tkach, Classical and quantum dynamics of particles with arbitrary spin, (In Russian), Pisma Zh. Eksp. Teor. Fiz. 29 (1979) 320 [Sov. Phys. JETP 29 (1979) 288] [SPIRES].Google Scholar
  10. [10]
    P.S. Howe, S. Penati, M. Pernici and P.K. Townsend, Wave equations for arbitrary spin from quantization of the extended supersymmetric spinning particle, Phys. Lett. B 215 (1988) 555 [SPIRES].MathSciNetADSGoogle Scholar
  11. [11]
    P.S. Howe, S. Penati, M. Pernici and P.K. Townsend, A particle mechanics description of antisymmetric tensor fields, Class. Quant. Grav. 6 (1989) 1125 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    D. Francia and A. Sagnotti, Free geometric equations for higher spins, Phys. Lett. B 543 (2002) 303 [hep-th/0207002] [SPIRES].MathSciNetADSGoogle Scholar
  13. [13]
    D. Francia and A. Sagnotti, On the geometry of higher-spin gauge fields, Class. Quant. Grav. 20 (2003) S473 [hep-th/0212185] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    D. Francia and A. Sagnotti, Minimal local lagrangians for higher-spin geometry, Phys. Lett. B 624 (2005) 93 [hep-th/0507144] [SPIRES].MathSciNetADSGoogle Scholar
  15. [15]
    D. Francia, J. Mourad and A. Sagnotti, Current exchanges and unconstrained higher spins, Nucl. Phys. B 773 (2007) 203 [hep-th/0701163] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    D. Francia, J. Mourad and A. Sagnotti, (A)dS exchanges and partially-massless higher spins, Nucl. Phys. B 804 (2008) 383 [arXiv:0803.3832] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    D. Francia, On the relation between local and geometric lagrangians for higher spins, J. Phys. Conf. Ser. 222 (2010) 012002 [arXiv:1001.3854] [SPIRES]. ADSCrossRefGoogle Scholar
  18. [18]
    S. Weinberg, Photons and gravitons in perturbation theory: Derivation of Maxwell’s and Einstein’s equations, Phys. Rev. 138 (1965) B988 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    B. de Wit and D.Z. Freedman, Systematics of higher spin gauge fields, Phys. Rev. D 21 (1980) 358 [SPIRES].ADSGoogle Scholar
  20. [20]
    T. Damour and S. Deser, ’geometry’ of spin 3 gauge theories, Ann. Poincaré 47 (1987) 277 [SPIRES].MathSciNetMATHGoogle Scholar
  21. [21]
    M. Dubois-Violette and M. Henneaux, Generalized cohomology for irreducible tensor fields of mixed Young symmetry type, Lett. Math. Phys. 49 (1999) 245 [math/9907135].MathSciNetMATHCrossRefGoogle Scholar
  22. [22]
    Tensor fields of mixed Young symmetry type and N-complexes, Commun. Math. Phys.226 (2002) 393 [math/0110088] [SPIRES].
  23. [23]
    C. Fronsdal, Massless fields with integer spin, Phys. Rev. D 18 (1978) 3624 [SPIRES]. ADSGoogle Scholar
  24. [24]
    C. Fronsdal, Singletons and massless, integral spin fields on de Sitter space (elementary particles in a curved space. 7, Phys. Rev. D 20 (1979) 848 [SPIRES].MathSciNetADSGoogle Scholar
  25. [25]
    J.M.F. Labastida and T.R. Morris, Massless mixed symmetry bosonic free fields, Phys. Lett. B 180 (1986) 101 [SPIRES].MathSciNetADSGoogle Scholar
  26. [26]
    J.M.F. Labastida, Massless bosonic free fields, Phys. Rev. Lett. 58 (1987) 531 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    J.M.F. Labastida, Massless particles in arbitrary representations of the Lorentz group, Nucl. Phys. B 322 (1989) 185 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    S. Ouvry and J. Stern, Gauge fields of any spin and symmetry, Phys. Lett. B 177 (1986) 335 [SPIRES].MathSciNetADSGoogle Scholar
  29. [29]
    W. Siegel and B. Zwiebach, Gauge string fields from the light cone, Nucl. Phys. B 282 (1987) 125 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  30. [30]
    J. Fang and C. Fronsdal, Massless fields with half integral spin, Phys. Rev. D 18 (1978) 3630 [SPIRES].ADSGoogle Scholar
  31. [31]
    T. Curtright, Massless field supermultiplets with arbitrary spin, Phys. Lett. B 85 (1979) 219 [SPIRES].ADSGoogle Scholar
  32. [32]
    J. Fang and C. Fronsdal, Massless, half integer spin fields in de Sitter space, Phys. Rev. D 22 (1980) 1361 [SPIRES].MathSciNetADSGoogle Scholar
  33. [33]
    R. Marnelius, Lagrangian higher spin field theories from the O(N) extended supersymmetric particle, arXiv:0906.2084 [SPIRES].
  34. [34]
    F. Bastianelli, O. Corradini and E. Latini, Higher spin fields from a worldline perspective, JHEP 02 (2007) 072 [hep-th/0701055] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  35. [35]
    F. Bastianelli and A. Zirotti, Worldline formalism in a gravitational background, Nucl. Phys. B 642 (2002) 372 [hep-th/0205182] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  36. [36]
    F. Bastianelli, O. Corradini and A. Zirotti, Dimensional regularization for SUSY σ-models and the worldline formalism, Phys. Rev. D 67 (2003) 104009 [hep-th/0211134] [SPIRES].ADSGoogle Scholar
  37. [37]
    F. Bastianelli, O. Corradini and A. Zirotti, BRST treatment of zero modes for the worldline formalism in curved space, JHEP 01 (2004) 023 [hep-th/0312064] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  38. [38]
    F. Bastianelli, P. Benincasa and S. Giombi, Worldline approach to vector and antisymmetric tensor fields, JHEP 04 (2005) 010 [hep-th/0503155] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  39. [39]
    F. Bastianelli, P. Benincasa and S. Giombi, Worldline approach to vector and antisymmetric tensor fields. II, JHEP 10 (2005) 114 [hep-th/0510010] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  40. [40]
    S.M. Kuzenko and Z.V. Yarevskaya, Conformal invariance, N-extended supersymmetry and massless spinning particles in Anti-de Sitter space, Mod. Phys. Lett. A 11 (1996) 1653 [hep-th/9512115] [SPIRES].MathSciNetADSGoogle Scholar
  41. [41]
    R. Marnelius, Manifestly conformal covariant description of spinning and charged particles, Phys. Rev. D 20 (1979) 2091 [SPIRES].ADSGoogle Scholar
  42. [42]
    W. Siegel, Conformal invariance of extended spinning particle mechanics, Int. J. Mod. Phys. A 3 (1988) 2713 [SPIRES].ADSGoogle Scholar
  43. [43]
    W. Siegel, All free conformal representations in all dimensions, Int. J. Mod. Phys. A 4 (1989) 2015 [SPIRES].ADSGoogle Scholar
  44. [44]
    R.R. Metsaev, All conformal invariant representations of d-dimensional anti-de Sitter group, Mod. Phys. Lett. A 10 (1995) 1719 [SPIRES].MathSciNetADSGoogle Scholar
  45. [45]
    X. Bekaert and M. Grigoriev, Manifestly conformal descriptions and higher symmetries of bosonic singletons, SIGMA 6 (2010) 038 [arXiv:0907.3195] [SPIRES].MathSciNetGoogle Scholar
  46. [46]
    F. Bastianelli, O. Corradini and E. Latini, Spinning particles and higher spin fields on (A)dS backgrounds, JHEP 11 (2008) 054 [arXiv:0810.0188] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  47. [47]
    R. Manvelyan and W. Rühl, The generalized curvature and Christoffel symbols for a higher spin potential in AdS d+1 space, Nucl. Phys. B 797 (2008) 371 [arXiv:0705.3528] [SPIRES].ADSCrossRefGoogle Scholar
  48. [48]
    R. Manvelyan and W. Rühl, Generalized curvature and Ricci tensors for a higher spin potential and the trace anomaly in external higher spin fields in AdS 4 space, Nucl. Phys. B 796 (2008) 457 [arXiv:0710.0952] [SPIRES].ADSGoogle Scholar
  49. [49]
    J. Engquist and O. Hohm, Geometry and dynamics of higher-spin frame fields, JHEP 04 (2008) 101 [arXiv:0708.1391] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  50. [50]
    I.A. Bandos and J. Lukierski, Tensorial central charges and new superparticle models with fundamental spinor coordinates, Mod. Phys. Lett. A 14 (1999) 1257 [hep-th/9811022] [SPIRES]. MathSciNetADSGoogle Scholar
  51. [51]
    I.A. Bandos, J. Lukierski and D.P. Sorokin, Superparticle models with tensorial central charges, Phys. Rev. D 61 (2000) 045002 [hep-th/9904109] [SPIRES].MathSciNetADSGoogle Scholar
  52. [52]
    I. Bandos, X. Bekaert, J.A. de Azcarraga, D. Sorokin and M. Tsulaia, Dynamics of higher spin fields and tensorial space, JHEP 05 (2005) 031 [hep-th/0501113] [SPIRES].ADSCrossRefGoogle Scholar
  53. [53]
    F. Bastianelli and R. Bonezzi, U(N) spinning particles and higher spin equations on complex manifolds, JHEP 03 (2009) 063 [arXiv:0901.2311] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  54. [54]
    F. Bastianelli and R. Bonezzi, U(N|M) quantum mechanics on Kähler manifolds, JHEP 05 (2010) 020 [arXiv:1003.1046] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  55. [55]
    F. Bastianelli, O. Corradini and A. Waldron, Detours and paths: BRST complexes and worldline formalism, JHEP 05 (2009) 017 [arXiv:0902.0530] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  56. [56]
    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] [SPIRES].MathSciNetADSGoogle Scholar
  57. [57]
    K.B. Alkalaev, M. Grigoriev and I.Y. Tipunin, Massless Poincaré modules and gauge invariant equations, Nucl. Phys. B 823 (2009) 509 [arXiv:0811.3999] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  58. [58]
    K.B. Alkalaev and M. Grigoriev, Unified BRST description of AdS gauge fields, Nucl. Phys. B 835 (2010) 197 [arXiv:0910.2690] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  59. [59]
    K. Hallowell and A. Waldron, Supersymmetric quantum mechanics and super-Lichnerowicz algebras, Commun. Math. Phys. 278 (2008) 775 [hep-th/0702033] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  60. [60]
    D. Cherney, E. Latini and A. Waldron, BRST detour quantization, J. Math. Phys. 51 (2010) 062302 [arXiv:0906.4814] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  61. [61]
    D. Cherney, E. Latini and A. Waldron, Generalized Einstein operator generating functions, Phys. Lett. B 682 (2010) 472 [arXiv:0909.4578] [SPIRES].MathSciNetADSGoogle Scholar
  62. [62]
    X. Bekaert and N. Boulanger, Tensor gauge fields in arbitrary representations of GL(D,R): duality and Poincaré lemma, Commun. Math. Phys. 245 (2004) 27 [hep-th/0208058] [SPIRES]. MathSciNetADSMATHCrossRefGoogle Scholar
  63. [63]
    X. Bekaert and N. Boulanger, On geometric equations and duality for free higher spins, Phys. Lett. B 561 (2003) 183 [hep-th/0301243] [SPIRES].MathSciNetADSGoogle Scholar
  64. [64]
    Y.M. Zinoviev, On massive mixed symmetry tensor fields in Minkowski space and (A)dS, hep-th/0211233 [SPIRES].
  65. [65]
    Y.M. Zinoviev, First order formalism for mixed symmetry tensor fields, hep-th/0304067 [SPIRES].
  66. [66]
    P. de Medeiros and C. Hull, Exotic tensor gauge theory and duality, Commun. Math. Phys. 235 (2003) 255 [hep-th/0208155] [SPIRES].ADSMATHCrossRefGoogle Scholar
  67. [67]
    P. de Medeiros and C. Hull, Geometric second order field equations for general tensor gauge fields, JHEP 05 (2003) 019 [hep-th/0303036] [SPIRES].CrossRefGoogle Scholar
  68. [68]
    K.B. Alkalaev, O.V. Shaynkman and M.A. Vasiliev, On the frame-like formulation of mixed-symmetry massless fields in (A)dS(d), Nucl. Phys. B 692 (2004) 363 [hep-th/0311164] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  69. [69]
    K.B. Alkalaev, Two-column higher spin massless fields in AdS(d), Theor. Math. Phys. 140 (2004) 1253 [Teor. Mat. Fiz. 140 (2004) 424] [hep-th/0311212] [SPIRES].MathSciNetMATHCrossRefGoogle Scholar
  70. [70]
    A. Campoleoni, D. Francia, J. Mourad and A. Sagnotti, Unconstrained higher spins of mixed symmetry. I. Bose fields, Nucl. Phys. B 815 (2009) 289 [arXiv:0810.4350] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  71. [71]
    A. Campoleoni, D. Francia, J. Mourad and A. Sagnotti, Unconstrained higher spins of mixed symmetry. II. Fermi fields, Nucl. Phys. B 828 (2010) 425 [arXiv:0904.4447] [SPIRES].MathSciNetADSGoogle Scholar
  72. [72]
    A. Campoleoni, Metric-like lagrangian formulations for higher-spin fields of mixed symmetry, Riv. Nuovo Cim. 033 (2010) 123 [arXiv:0910.3155] [SPIRES].Google Scholar
  73. [73]
    I.L. Buchbinder, A. Pashnev and M. Tsulaia, Lagrangian formulation of the massless higher integer spin fields in the AdS background, Phys. Lett. B 523 (2001) 338 [hep-th/0109067] [SPIRES]. MathSciNetADSGoogle Scholar
  74. [74]
    A. Sagnotti and M. Tsulaia, On higher spins and the tensionless limit of string theory, Nucl. Phys. B 682 (2004) 83 [hep-th/0311257] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  75. [75]
    I.L. Buchbinder, V.A. Krykhtin and A.A. Reshetnyak, BRST approach to lagrangian construction for fermionic higher spin fields in AdS space, Nucl. Phys. B 787 (2007) 211 [hep-th/0703049] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  76. [76]
    G. Bonelli, On the covariant quantization of tensionless bosonic strings in AdS spacetime, JHEP 11 (2003) 028 [hep-th/0309222] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  77. [77]
    V. Bargmann and E.P. Wigner, Group theoretical discussion of relativistic wave equations, Proc. Nat. Acad. Sci. 34 (1948) 211 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  78. [78]
    R. Marnelius and U. Martensson, BRST quantization of free massless relativistic particles of arbitrary spin, Nucl. Phys. B 321 (1989) 185 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  79. [79]
    W. Siegel, Fields, hep-th/9912205 [SPIRES].
  80. [80]
    I.L. Buchbinder and V.A. Krykhtin, BRST lagrangian construction for spin-3/2 field in Einstein space, Mod. Phys. Lett. A 25 (2010) 1667 [arXiv:1003.0185] [SPIRES].MathSciNetADSGoogle Scholar
  81. [81]
    I.L. Buchbinder, V.A. Krykhtin and P.M. Lavrov, BRST lagrangian construction for spin-2 field on the gravitation background with nontrivial Weyl tensor, Phys. Lett. B 685 (2010) 208 [arXiv:0912.0611] [SPIRES].MathSciNetADSGoogle Scholar
  82. [82]
    D. Francia, Geometric lagrangians for massive higher-spin fields, Nucl. Phys. B 796 (2008) 77 [arXiv:0710.5378] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  83. [83]
    S. Deser and A. Waldron, Gauge invariances and phases of massive higher spins in (A)dS, Phys. Rev. Lett. 87 (2001) 031601 [hep-th/0102166] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  84. [84]
    Y.M. Zinoviev, On massive high spin particles in (A)dS, hep-th/0108192 [SPIRES].
  85. [85]
    P. de Medeiros, Massive gauge-invariant field theories on spaces of constant curvature, Class. Quant. Grav. 21 (2004) 2571 [hep-th/0311254] [SPIRES].ADSMATHCrossRefGoogle Scholar
  86. [86]
    R.R. Metsaev, Massive totally symmetric fields in AdS(d), Phys. Lett. B 590 (2004) 95 [hep-th/0312297] [SPIRES].MathSciNetADSGoogle Scholar
  87. [87]
    R.R. Metsaev, Mixed symmetry massive fields in AdS 5, Class. Quant. Grav. 22 (2005) 2777 [hep-th/0412311] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  88. [88]
    I.L. Buchbinder and V.A. Krykhtin, Gauge invariant Lagrangian construction for massive bosonic higher spin fields in D dimensions, Nucl. Phys. B 727 (2005) 537 [hep-th/0505092] [SPIRES]. MathSciNetADSCrossRefGoogle Scholar
  89. [89]
    I.L. Buchbinder, V.A. Krykhtin, L.L. Ryskina and H. Takata, Gauge invariant lagrangian construction for massive higher spin fermionic fields, Phys. Lett. B 641 (2006) 386 [hep-th/0603212] [SPIRES].MathSciNetADSGoogle Scholar
  90. [90]
    I.L. Buchbinder and A.V. Galajinsky, Quartet unconstrained formulation for massive higher spin fields, JHEP 11 (2008) 081 [arXiv:0810.2852] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  91. [91]
    E.A. Bergshoeff, O. Hohm and P.K. Townsend, On higher derivatives in 3D gravity and higher spin gauge theories, Annals Phys. 325 (2010) 1118 [arXiv:0911.3061] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  92. [92]
    M.S. Plyushchay, Fractional spin: Majorana-Dirac field, Phys. Lett. B 273 (1991) 250 [SPIRES].MathSciNetADSGoogle Scholar
  93. [93]
    M.S. Plyushchay, The model of a free relativistic particle with fractional spin, Int. J. Mod. Phys. A 7 (1992) 7045 [SPIRES].MathSciNetADSMATHGoogle Scholar

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© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Dipartimento di FisicaUniversità di BolognaBolognaItaly
  2. 2.INFN, Sezione di BolognaBolognaItaly
  3. 3.Centro de Estudios en Física y Matemáticas Basicas y AplicadasUniversidad Autónoma de ChiapasChiapasMexico

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