Journal of High Energy Physics

, Volume 2015, Issue 12, pp 1–27 | Cite as

BRST analysis of the supersymmetric higher spin field models

Open Access
Regular Article - Theoretical Physics

Abstract

We develop the BRST approach for all massless integer and half-integer higher spins in 4D Minkowski space, using the two component spinor notation and develop the Lagrangian formulation for supersymmetric higher spin models. It is shown that the problem of second class constraints disappears and the BRST procedure becomes much more simple than in tensorial notation. Furthermore, we demonstrate that the BRST procedure automatically provides extra auxiliary components that belong in the set of supersymmetry auxiliary components. Finally, we demonstrate how supersymmetry transformations transformations are realized in such an approach. As a result, we conclude that the BRST approach to higher spin supersymmetric theories allows to derive both the Lagrangian and the supersymmetry transformations. Although most part of the work is devoted to massless component supersymmetric models, we also discuss generalization for massive component supersymmetric models and for superfield models.

Keywords

Higher Spin Symmetry Supersymmetric Effective Theories BRST Symmetry 

References

  1. [1]
    J. Wess and J. Bagger, Supersymmetry and Supergravity, Princeton University Press, Princeton U.S.A. (1983).MATHGoogle Scholar
  2. [2]
    P. West, Introduction to Supersymmetry and Supergravity, World Scientific, Singapore (1986).CrossRefMATHGoogle Scholar
  3. [3]
    A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic superspace, Cambridge University Press, Cambridge U.K. (2001).CrossRefMATHGoogle Scholar
  4. [4]
    S.J. Gates, M.T. Grisaru, M. Roćek, W. Siegel, Superspace or one Thousand and One Lessons in Supersymmetry, Benjamin Cummings, Reading U.S.A. (1983).MATHGoogle Scholar
  5. [5]
    I.L. Buchbinder and S.M. Kuzenko, Ideas and Methods of Supersymmetry and Superfravity or a Walk Through Superspace, IOP Publishing, Bristol U.K. (1998).MATHGoogle Scholar
  6. [6]
    M. Dress, R.M. Godbole and P. Roy, Sparticles. An account of four-dimensional \( \mathcal{N}=1 \) supersymmetry in High Energy Physics, World Scientific, New York U.S.A. (2004).Google Scholar
  7. [7]
    P. Binetruy, Supersymmetry: Theory, Experiment, Cosmology, Oxford University Press, Oxford U.K. (2006).MATHGoogle Scholar
  8. [8]
    J. Terning, Modern Supersymmetry, Clarendon Press, Oxford U.K. (2006).MATHGoogle Scholar
  9. [9]
    M. Dine, Supersymmetry and String Theory: Beyond the Standrad Model, Cambridge University Press, Cambridge U.K. (2007).CrossRefMATHGoogle Scholar
  10. [10]
    M.A. Vasiliev, Higher spin gauge theories in various dimensions, Fortsch. Phys. 52 (2004) 702 [hep-th/0401177] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    D. Sorokin, Introduction to the classical theory of higher spins, AIP Conf. Proc. 767 (2005) 172 [hep-th/0405069] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    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] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, hep-th/0503128 [INSPIRE].
  14. [14]
    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].ADSCrossRefGoogle Scholar
  15. [15]
    A. Sagnotti, Notes on Strings and Higher Spins, J. Phys. A 46 (2013) 214006 [arXiv:1112.4285] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  16. [16]
    V.E. Didenko and E.D. Skvortsov, Elements of Vasiliev theory, arXiv:1401.2975 [INSPIRE].
  17. [17]
    M.A. Vasiliev, Higher-Spin Theory and Space-Time Metamorphoses, Lect. Notes Phys. 892 (2015) 227 [arXiv:1404.1948] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    T. Curtright, Massless Field Supermultiplets With Arbitrary Spin, Phys. Lett. B 85 (1979) 219 [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    S.M. Kuzenko, A.G. Sibiryakov and V.V. Postnikov, Massless gauge superfields of higher half integer superspins, JETP Lett. 57 (1993) 534 [INSPIRE].ADSGoogle Scholar
  20. [20]
    S.M. Kuzenko and A.G. Sibiryakov, Massless gauge superfields of higher integer superspins, JETP Lett. 57 (1993) 539 [INSPIRE].ADSGoogle Scholar
  21. [21]
    S.M. Kuzenko and A.G. Sibiryakov, Free massless higher superspin superfields on the anti-de Sitter superspace, Phys. Atom. Nucl. 57 (1994) 1257 [arXiv:1112.4612] [INSPIRE].ADSGoogle Scholar
  22. [22]
    S.J. Gates Jr., S.M. Kuzenko and A.G. Sibiryakov, \( \mathcal{N}=2 \) supersymmetry of higher superspin massless theories, Phys. Lett. B 412 (1997) 59 [hep-th/9609141] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    S.J. Gates Jr., S.M. Kuzenko and A.G. Sibiryakov, Towards a unified theory of massless superfields of all superspins, Phys. Lett. B 394 (1997) 343 [hep-th/9611193] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    S.J. Gates Jr. and K. Koutrolikos, On 4D, \( \mathcal{N}=1 \) massless gauge superfields of arbitrary superhelicity, JHEP 06 (2014) 098 [arXiv:1310.7385] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    Yu. M. Zinoviev, Massive \( \mathcal{N}=1 \) supermultiplets with arbitrary superspins, Nucl. Phys. B 785 (2007) 98 [arXiv:0704.1535] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    I.L. Buchbinder, T.V. Snegirev and Yu. M. Zinoviev, Lagrangian formulation of the massive higher spin supermultiplets in three dimensional space-time, JHEP 10 (2015) 148 [arXiv:1508.02829] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    I.L. Buchbinder, S.J. Gates Jr., W.D. Linch, III and J. Phillips, New 4D, \( \mathcal{N}=1 \) superfield theory: Model of free massive superspin-3/2 multiplet, Phys. Lett. B 535 (2002) 280 [hep-th/0201096] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  28. [28]
    I.L. Buchbinder, S.J. Gates Jr., W.D. Linch, III and J. Phillips, Dynamical superfield theory of free massive superspin-1 multiplet, Phys. Lett. B 549 (2002) 229 [hep-th/0207243] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    I.L. Buchbinder, S.J. Gates Jr., S.M. Kuzenko and J. Phillips, Massive 4D, \( \mathcal{N}=1 \) superspin 1 and 3/2 multiplets and dualities, JHEP 02 (2005) 056 [hep-th/0501199] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    S.J. Gates Jr. and K. Koutrolikos, A dynamical theory for linearized massive superspin 3/2, JHEP 03 (2014) 030 [arXiv:1310.7387] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    E.S. Fradkin and G.A. Vilkovisky, Quantization of relativistic systems with constraints, Phys. Lett. B 55 (1975) 224 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    I.A. Batalin and G.A. Vilkovisky, Relativistic S Matrix of Dynamical Systems with Boson and Fermion Constraints, Phys. Lett. B 69 (1977) 309 [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    E.S. Fradkin and T.E. Fradkina, Quantization of Relativistic Systems with Boson and Fermion First and Second Class Constraints, Phys. Lett. B 72 (1978) 343 [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    I.A. Batalin and E.S. Fradkin, Operator Quantization of Relativistic Dynamical Systems Subject to First Class Constraints, Phys. Lett. B 128 (1983) 303 [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    M. Henneaux, Hamiltonian Form of the Path Integral for Theories with a Gauge Freedom, Phys. Rept. 126 (1985) 1 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    I.A. Batalin and E.S. Fradkin, Operatorial quantizaion of dynamical systems subject to constraints. A Further study of the construction, Annales Poincare Phys. Theor. 49 (1988) 145.Google Scholar
  37. [37]
    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] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  38. [38]
    X. Bekaert, I.L. Buchbinder, A. Pashnev and M. Tsulaia, On higher spin theory: Strings, BRST, dimensional reductions, Class. Quant. Grav. 21 (2004) S1457 [hep-th/0312252] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  39. [39]
    I.L. Buchbinder, A. Fotopoulos, A.C. Petkou and M. Tsulaia, Constructing the cubic interaction vertex of higher spin gauge fields, Phys. Rev. D 74 (2006) 105018 [hep-th/0609082] [INSPIRE].ADSMathSciNetGoogle Scholar
  40. [40]
    A. Fotopoulos, N. Irges, A.C. Petkou and M. Tsulaia, Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex, JHEP 10 (2007) 021 [arXiv:0708.1399] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  41. [41]
    I.L. Buchbinder, P. Dempster and M. Tsulaia, Massive Higher Spin Fields Coupled to a Scalar: Aspects of Interaction and Causality, Nucl. Phys. B 877 (2013) 260 [arXiv:1308.5539] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  42. [42]
    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] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  43. [43]
    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] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  44. [44]
    I.L. Buchbinder, V.A. Krykhtin and P.M. Lavrov, Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space, Nucl. Phys. B 762 (2007) 344 [hep-th/0608005] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  45. [45]
    I.L. Buchbinder, V.A. Krykhtin and A. Pashnev, BRST approach to Lagrangian construction for fermionic massless higher spin fields, Nucl. Phys. B 711 (2005) 367 [hep-th/0410215] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  46. [46]
    I.L. Buchbinder, A.V. Galajinsky and V.A. Krykhtin, Quartet unconstrained formulation for massless higher spin fields, Nucl. Phys. B 779 (2007) 155 [hep-th/0702161] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  47. [47]
    I.L. Buchbinder, V.A. Krykhtin and A.A. Reshetnyak, BRST approach to Lagrangian construction for fermionic higher spin fields in (A)dS space, Nucl. Phys. B 787 (2007) 211 [hep-th/0703049] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  48. [48]
    I.L. Buchbinder, V.A. Krykhtin and H. Takata, Gauge invariant Lagrangian construction for massive bosonic mixed symmetry higher spin fields, Phys. Lett. B 656 (2007) 253 [arXiv:0707.2181] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  49. [49]
    I.L. Buchbinder, V.A. Krykhtin and M. Tsulaia, Lagrangian formulation of massive fermionic higher spin fields on a constant electromagnetic background, Nucl. Phys. B 896 (2015) 1 [arXiv:1501.03278] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  50. [50]
    I.L. Buchbinder and V.A. Krykhtin, Quartic interaction vertex in the massive integer higher spin field theory in a constant electromagnetic field, Eur. Phys. J. C 75 (2015) 454 [arXiv:1507.03723] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    O.A. Gelfond and M.A. Vasiliev, Sp(8) invariant higher spin theory, twistors and geometric BRST formulation of unfolded field equations, JHEP 12 (2009) 021 [arXiv:0901.2176] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  52. [52]
    O.A. Gelfond and M.A. Vasiliev, Unfolding Versus BRST and Currents in Sp(2M) Invariant Higher-Spin Theory, arXiv:1001.2585 [INSPIRE].
  53. [53]
    K.B. Alkalaev and M. Grigoriev, Unified BRST description of AdS gauge fields, Nucl. Phys. B 835 (2010) 197 [arXiv:0910.2690] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  54. [54]
    M. Grigoriev and A. Waldron, Massive Higher Spins from BRST and Tractors, Nucl. Phys. B 853 (2011) 291 [arXiv:1104.4994] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  55. [55]
    K. Alkalaev and M. Grigoriev, Unified BRST approach to (partially) massless and massive AdS fields of arbitrary symmetry type, Nucl. Phys. B 853 (2011) 663 [arXiv:1105.6111] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  56. [56]
    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].ADSMathSciNetCrossRefGoogle Scholar
  57. [57]
    R.R. Metsaev, BRST invariant effective action of shadow fields, conformal fields and AdS/CFT, Theor. Math. Phys. 181 (2014) 1548 [arXiv:1407.2601] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  58. [58]
    R.R. Metsaev, BRST-BV approach to massless fields adapted to AdS/CFT correspondence, arXiv:1508.07928 [INSPIRE].
  59. [59]
    I.A. Batalin and I.V. Tyutin, Existence theorem for the effective gauge algebra in the generalized canonical formalism with Abelian conversion of second class constraints, Int. J. Mod. Phys. A 6 (1991) 3255 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  60. [60]
    E.S. Egorian and R.P. Manvelyan, Quantization of dynamical systems with first and second class constraints, Theor. Math. Phys. 94 (1993) 173 [INSPIRE].CrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsTomsk State Pedagogical UniversityTomskRussia
  2. 2.National Research Tomsk State UniversityTomskRussia
  3. 3.Physics DivisionNational Technical University of AthensAthensGreece
  4. 4.Institute for Theoretical Physics & AstrophysicsMasaryk UniversityBrnoCzech Republic

Personalised recommendations