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Generating functions of (partially-)massless higher-spin cubic interactions

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Abstract

Generating functions encoding cubic interactions of (partially-)massless higher-spin fields are provided within the ambient-space formalism. They satisfy a system of higher-order partial differential equations that can be explicitly solved due to their factorized form. We find that the number of consistent couplings increases whenever the squares of the field masses take some integer values (in units of the cosmological constant) and satisfy certain conditions. Moreover, it is shown that only the supplemental solutions can give rise to non-Abelian deformations of the gauge symmetries. The presence of these conditions on the masses is a distinctive feature of (A)dS interactions that has in general no direct counterpart in flat space.

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References

  1. 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].

    Article  ADS  Google Scholar 

  2. A. Sagnotti, Notes on strings and higher spins, arXiv:1112.4285 [INSPIRE].

  3. M. Vasiliev, Higher spin gauge theories in any dimension, Comptes Rendus Physique 5 (2004) 1101 [hep-th/0409260] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. X. Bekaert, S. Cnockaert, C. Iazeolla and M. Vasiliev, Nonlinear higher spin theories in various dimensions, hep-th/0503128 [INSPIRE].

  5. S. Giombi and X. Yin, The higher spin/vector model duality, arXiv:1208.4036 [INSPIRE].

  6. M.R. Gaberdiel and R. Gopakumar, Minimal model holography, arXiv:1207.6697 [INSPIRE].

  7. M. Ammon, M. Gutperle, P. Kraus and E. Perlmutter, Black holes in three dimensional higher spin gravity: a review, arXiv:1208.5182 [INSPIRE].

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

    Article  MathSciNet  ADS  Google Scholar 

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

    ADS  Google Scholar 

  10. M.A. Vasiliev, Consistent equations for interacting massless fields of all spins in the first order in curvatures, Annals Phys. 190 (1989) 59 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  12. X. Bekaert, N. Boulanger and S. Leclercq, Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex, J. Phys. A 43 (2010) 185401 [arXiv:1002.0289] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  13. R. Manvelyan, K. Mkrtchyan and W. Ruehl, Direct construction of a cubic selfinteraction for higher spin gauge fields, Nucl. Phys. B 844 (2011) 348 [arXiv:1002.1358] [INSPIRE].

    Article  ADS  Google Scholar 

  14. R. Manvelyan, K. Mkrtchyan and W. Rühl, General trilinear interaction for arbitrary even higher spin gauge fields, Nucl. Phys. B 836 (2010) 204 [arXiv:1003.2877] [INSPIRE].

    Article  ADS  Google Scholar 

  15. M. Taronna, Higher spins and string interactions, arXiv:1005.3061 [INSPIRE].

  16. D. Polyakov, Gravitational couplings of higher spins from string theory, Int. J. Mod. Phys. A 25 (2010) 4623 [arXiv:1005.5512] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  17. A. Sagnotti and M. Taronna, String lessons for higher-spin interactions, Nucl. Phys. B 842 (2011) 299 [arXiv:1006.5242] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. A. Fotopoulos and M. Tsulaia, On the tensionless limit of string theory, off - Shell higher spin interaction vertices and BCFW recursion relations, JHEP 11 (2010) 086 [arXiv:1009.0727] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. R. Manvelyan, K. Mkrtchyan and W. Ruehl, A generating function for the cubic interactions of higher spin fields, Phys. Lett. B 696 (2011) 410 [arXiv:1009.1054] [INSPIRE].

    ADS  Google Scholar 

  20. S. Lee and D. Polyakov, String amplitudes and frame-like formalism for higher spins, Phys. Rev. D 85 (2012) 106014 [arXiv:1203.0909] [INSPIRE].

    ADS  Google Scholar 

  21. I. Buchbinder, T. Snegirev and Y. Zinoviev, Cubic interaction vertex of higher-spin fields with external electromagnetic field, Nucl. Phys. B 864 (2012) 694 [arXiv:1204.2341] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. R. Metsaev, BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields, arXiv:1205.3131 [INSPIRE].

  23. M. Henneaux, G. Lucena Gomez and R. Rahman, Higher-spin fermionic gauge fields and their electromagnetic coupling, JHEP 08 (2012) 093 [arXiv:1206.1048] [INSPIRE].

    Article  ADS  Google Scholar 

  24. Y. Zinoviev, Spin 3 cubic vertices in a frame-like formalism, JHEP 08 (2010) 084 [arXiv:1007.0158] [INSPIRE].

    Article  ADS  Google Scholar 

  25. X. Bekaert and E. Meunier, Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions, JHEP 11 (2010) 116 [arXiv:1007.4384] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. D. Polyakov, A string model for AdS gravity and higher spins, Phys. Rev. D 84 (2011) 126004 [arXiv:1106.1558] [INSPIRE].

    ADS  Google Scholar 

  27. M. Vasiliev, Cubic vertices for symmetric higher-spin gauge fields in (A)dS d , Nucl. Phys. B 862 (2012) 341 [arXiv:1108.5921] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. D. Polyakov, Higher spin holography and AdS string σ-model, arXiv:1207.4751 [INSPIRE].

  29. R. Manvelyan, R. Mkrtchyan and W. Ruehl, Radial reduction and cubic interaction for higher spins in (A)dS space, arXiv:1210.7227 [INSPIRE].

  30. N. Boulanger, D. Ponomarev and E. Skvortsov, Non-abelian cubic vertices for higher-spin fields in Anti-de Sitter space, arXiv:1211.6979 [INSPIRE].

  31. D. Polyakov, Higher spins and open strings: quartic interactions, Phys. Rev. D 83 (2011) 046005 [arXiv:1011.0353] [INSPIRE].

    ADS  Google Scholar 

  32. M. Taronna, Higher-spin interactions: four-point functions and beyond, JHEP 04 (2012) 029 [arXiv:1107.5843] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. P. Dempster and M. Tsulaia, On the structure of quartic vertices for massless higher spin fields on Minkowski background, Nucl. Phys. B 865 (2012) 353 [arXiv:1203.5597] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. E. Joung and M. Taronna, Cubic interactions of massless higher spins in (A)dS: metric-like approach, Nucl. Phys. B 861 (2012) 145 [arXiv:1110.5918] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. E. Joung, L. Lopez and M. Taronna, On the cubic interactions of massive and partially-massless higher spins in (A)dS, JHEP 07 (2012) 041 [arXiv:1203.6578] [INSPIRE].

    Article  ADS  Google Scholar 

  36. E. Joung, L. Lopez and M. Taronna, Solving the Noether procedure for cubic interactions of higher spins in (A)dS, arXiv:1207.5520 [INSPIRE].

  37. M. Taronna, Higher-spin interactions: three-point functions and beyond, arXiv:1209.5755 [INSPIRE].

  38. 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 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  39. T. Biswas and W. Siegel, Radial dimensional reduction: Anti-de Sitter theories from flat, JHEP 07 (2002) 005 [hep-th/0203115] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. L. Lopez, On cubic AdS interactions of mixed-symmetry higher spins, arXiv:1210.0554 [INSPIRE].

  41. S. Deser and R.I. Nepomechie, Gauge invariance versus masslessness in de Sitter space, Annals Phys. 154 (1984) 396 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. S. Deser and R.I. Nepomechie, Anomalous propagation of gauge fields in conformally flat spaces, Phys. Lett. B 132 (1983) 321 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  43. A. Higuchi, Forbidden mass range for spin-2 field theory in de Sitter space-time, Nucl. Phys. B 282 (1987) 397 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. A. Higuchi, Symmetric tensor spherical harmonics on the N sphere and their application to the de Sitter group SO(N, 1), J. Math. Phys. 28 (1987) 1553 [Erratum ibid. 43 (2002) 6385] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  45. A. Higuchi, Massive symmetric tensor field in space-times with a positive cosmological constant, Nucl. Phys. B 325 (1989) 745 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. S. Deser and A. Waldron, (Dis)continuities of massless limits in spin 3/2 mediated interactions and cosmological supergravity, Phys. Lett. B 501 (2001) 134 [hep-th/0012014] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  47. S. Deser and A. Waldron, Stability of massive cosmological gravitons, Phys. Lett. B 508 (2001) 347 [hep-th/0103255] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  48. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  50. S. Deser and A. Waldron, Null propagation of partially massless higher spins in (A)dS and cosmological constant speculations, Phys. Lett. B 513 (2001) 137 [hep-th/0105181] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

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

  52. L. Dolan, C.R. Nappi and E. Witten, Conformal operators for partially massless states, JHEP 10 (2001) 016 [hep-th/0109096] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  53. S. Deser and A. Waldron, Arbitrary spin representations in de Sitter from dS/CFT with applications to dS supergravity, Nucl. Phys. B 662 (2003) 379 [hep-th/0301068] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  55. A. Gover, A. Shaukat and A. Waldron, Weyl invariance and the origins of mass, Phys. Lett. B 675 (2009) 93 [arXiv:0812.3364] [INSPIRE].

    ADS  Google Scholar 

  56. E. Skvortsov, Gauge fields in (A)dS(d) and connections of its symmetry algebra, J. Phys. A 42 (2009) 385401 [arXiv:0904.2919] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  57. K.B. Alkalaev and M. Grigoriev, Unified BRST description of AdS gauge fields, Nucl. Phys. B 835 (2010) 197 [arXiv:0910.2690] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  58. E. Skvortsov, Gauge fields in (A)dS(d) within the unfolded approach: algebraic aspects, JHEP 01 (2010) 106 [arXiv:0910.3334] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. 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].

    Article  MathSciNet  ADS  Google Scholar 

  60. S. Deser and A. Waldron, Partially massless spin 2 electrodynamics, Phys. Rev. D 74 (2006) 084036 [hep-th/0609113] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  61. Y. Zinoviev, On massive spin 2 interactions, Nucl. Phys. B 770 (2007) 83 [hep-th/0609170] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  62. D. Francia, J. Mourad and A. Sagnotti, (A)dS exchanges and partially-massless higher spins, Nucl. Phys. B 804 (2008) 383 [arXiv:0803.3832] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  63. S. Deser, E. Joung and A. Waldron, Gravitational and self-coupling of partially massless spin 2, Phys. Rev. D 86 (2012) 104004 [arXiv:1208.1307] [INSPIRE].

    ADS  Google Scholar 

  64. E. Joung and K. Mkrtchyan, A note on higher-derivative actions for free higher-spin fields, JHEP 11 (2012) 153 [arXiv:1209.4864] [INSPIRE].

    Article  ADS  Google Scholar 

  65. C. de Rham and S. Renaux-Petel, Massive gravity on de Sitter and unique candidate for partially massless gravity, arXiv:1206.3482 [INSPIRE].

  66. M. Fasiello and A.J. Tolley, Cosmological perturbations in massive gravity and the Higuchi bound, JCAP 11 (2012) 035 [arXiv:1206.3852] [INSPIRE].

    Article  ADS  Google Scholar 

  67. S. Hassan, A. Schmidt-May and M. von Strauss, On partially massless bimetric gravity, arXiv:1208.1797 [INSPIRE].

  68. J. Dixmier, Représentations intégrables du groupe de de Sitter, Bull. Soc. Math. France 89 (1961) 9.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Scuola Normale Superiore and INFN, Piazza dei Cavalieri 7, 56126, Pisa, Italy

    Euihun Joung, Luca Lopez & Massimo Taronna

  2. Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Am Mühlenberg 1, 14476, Golm, Germany

    Massimo Taronna

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  1. Euihun Joung
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  2. Luca Lopez
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  3. Massimo Taronna
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Correspondence to Massimo Taronna.

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ArXiv ePrint: 1211.5912

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Joung, E., Lopez, L. & Taronna, M. Generating functions of (partially-)massless higher-spin cubic interactions. J. High Energ. Phys. 2013, 168 (2013). https://doi.org/10.1007/JHEP01(2013)168

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