Advertisement

A bound on massive higher spin particles

  • Nima Afkhami-Jeddi
  • Sandipan KunduEmail author
  • Amirhossein Tajdini
Open Access
Regular Article - Theoretical Physics
  • 15 Downloads

Abstract

According to common lore, massive elementary higher spin particles lead to inconsistencies when coupled to gravity. However, this scenario was not completely ruled out by previous arguments. In this paper, we show that in a theory where the low energy dynamics of the gravitons are governed by the Einstein-Hilbert action, any finite number of massive elementary particles with spin more than two cannot interact with gravitons, even classically, in a way that preserves causality. This is achieved in flat spacetime by studying eikonal scattering of higher spin particles in more than three spacetime dimensions. Our argument is insensitive to the physics above the effective cut-off scale and closes certain loopholes in previous arguments. Furthermore, it applies to higher spin particles even if they do not contribute to tree-level graviton scattering as a consequence of being charged under a global symmetry such as ℤ2. We derive analogous bounds in anti-de Sitter space-time from analyticity properties of correlators of the dual CFT in the Regge limit. We also argue that an infinite tower of fine-tuned higher spin particles can still be consistent with causality. However, they necessarily affect the dynamics of gravitons at an energy scale comparable to the mass of the lightest higher spin particle. Finally, we apply the bound in de Sitter to impose restrictions on the structure of three-point functions in the squeezed limit of the scalar curvature perturbation produced during inflation.

Keywords

AdS-CFT Correspondence Conformal Field Theory Effective Field Theories Models of Quantum Gravity 

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]
    S. Weinberg, Photons and gravitons in s matrix theory: derivation of charge conservation and equality of gravitational and inertial mass, Phys. Rev. 135 (1964) B1049 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    S. Weinberg and E. Witten, Limits on massless particles, Phys. Lett. B 96 (1980) 59.Google Scholar
  3. [3]
    M. Porrati, Universal limits on massless high-spin particles, Phys. Rev. D 78 (2008) 065016 [arXiv:0804.4672] [INSPIRE].
  4. [4]
    N. Arkani-Hamed, T.-C. Huang and Y.-t. Huang, Scattering amplitudes for all masses and spins, arXiv:1709.04891 [INSPIRE].
  5. [5]
    S. Weinberg, Lectures on elementary particles and quantum field theory, S. Deser ed., MIT Press, Cambridge U.S.A. (1970).Google Scholar
  6. [6]
    S. Ferrara, M. Porrati and V.L. Telegdi, g = 2 as the natural value of the tree-level gyromagnetic ratio of elementary particles, Phys. Rev. D 46 (1992) 3529 [INSPIRE].
  7. [7]
    M. Porrati, Massive spin 5/2 fields coupled to gravity: tree level unitarity versus the equivalence principle, Phys. Lett. B 304 (1993) 77 [gr-qc/9301012] [INSPIRE].
  8. [8]
    A. Cucchieri, M. Porrati and S. Deser, Tree level unitarity constraints on the gravitational couplings of higher spin massive fields, Phys. Rev. D 51 (1995) 4543 [hep-th/9408073] [INSPIRE].
  9. [9]
    X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality constraints on corrections to the graviton three-point coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    M.A. Vasiliev, Higher spin gauge theories in various dimensions, Fortsch. Phys. 52 (2004) 702 [hep-th/0401177] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    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, pp. 132-197, 2004, hep-th/0503128 [INSPIRE].
  13. [13]
    M.T. Grisaru and H.N. Pendleton, Soft spin 3/2 fermions require gravity and supersymmetry, Phys. Lett. B 67 (1977) 323.Google Scholar
  14. [14]
    M.T. Grisaru, H.N. Pendleton and P. van Nieuwenhuizen, Supergravity and the S matrix, Phys. Rev. D 15 (1977) 996 [INSPIRE].
  15. [15]
    F. Loebbert, The Weinberg-Witten theorem on massless particles: An Essay, Annalen Phys. 17 (2008) 803 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  16. [16]
    C. Aragone and S. Deser, Consistency problems of hypergravity, Phys. Lett. B 86 (1979) 161.Google Scholar
  17. [17]
    F.A. Berends, J.W. van Holten, P. van Nieuwenhuizen and B. de Wit, On spin 5/2 gauge fields, Phys. Lett. B 83 (1979) 188 [Erratum ibid. B 84 (1979) 529].Google Scholar
  18. [18]
    C. Aragone and H. La Roche, Massless second order tetradic spin 3 fields and higher helicity bosons, Nuovo Cim. A 72 (1982) 149 [INSPIRE].
  19. [19]
    R.R. Metsaev, Cubic interaction vertices of massive and massless higher spin fields, Nucl. Phys. B 759 (2006) 147 [hep-th/0512342] [INSPIRE].
  20. [20]
    N. Boulanger and S. Leclercq, Consistent couplings between spin-2 and spin-3 massless fields, JHEP 11 (2006) 034 [hep-th/0609221] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    N. Boulanger, S. Leclercq and P. Sundell, On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory, JHEP 08 (2008) 056 [arXiv:0805.2764] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    A. Adams et al., Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from conformal field theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    L. Cornalba, M.S. Costa, J. Penedones and R. Schiappa, Eikonal approximation in AdS/CFT: from shock waves to four-point functions, JHEP 08 (2007) 019 [hep-th/0611122] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    L. Cornalba, M.S. Costa, J. Penedones and R. Schiappa, Eikonal approximation in AdS/CFT: conformal partial waves and finite N four-point functions, Nucl. Phys. B 767 (2007) 327 [hep-th/0611123] [INSPIRE].
  26. [26]
    L. Cornalba, M.S. Costa and J. Penedones, Eikonal approximation in AdS/CFT: Resumming the gravitational loop expansion, JHEP 09 (2007) 037 [arXiv:0707.0120] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    G. Mack, D-dimensional conformal field theories with anomalous dimensions as dual resonance models, Bulg. J. Phys. 36 (2009) 214 [arXiv:0909.1024] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  28. [28]
    G. Mack, D-independent representation of conformal field theories in D dimensions via transformation to auxiliary dual resonance models. Scalar amplitudes, arXiv:0907.2407 [INSPIRE].
  29. [29]
    A.L. Fitzpatrick, E. Katz, D. Poland and D. Simmons-Duffin, Effective conformal theory and the flat-space limit of AdS, JHEP 07 (2011) 023 [arXiv:1007.2412] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    I. Heemskerk and J. Sully, More holography from conformal field theory, JHEP 09 (2010) 099 [arXiv:1006.0976] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    A.L. Fitzpatrick and J. Kaplan, Analyticity and the holographic S-matrix, JHEP 10 (2012) 127 [arXiv:1111.6972] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  32. [32]
    A.L. Fitzpatrick et al., A natural language for AdS/CFT correlators, JHEP 11 (2011) 095 [arXiv:1107.1499] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    S. El-Showk and K. Papadodimas, Emergent spacetime and holographic CFTs, JHEP 10 (2012) 106 [arXiv:1101.4163] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    Z. Komargodski and A. Zhiboedov, Convexity and liberation at large spin, JHEP 11 (2013) 140 [arXiv:1212.4103] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    A.L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, The analytic bootstrap and AdS superhorizon locality, JHEP 12 (2013) 004 [arXiv:1212.3616] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    A.L. Fitzpatrick and J. Kaplan, AdS field theory from conformal field theory, JHEP 02 (2013) 054 [arXiv:1208.0337] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    V. Goncalves, J. Penedones and E. Trevisani, Factorization of Mellin amplitudes, JHEP 10 (2015) 040 [arXiv:1410.4185] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    E. Hijano, P. Kraus, E. Perlmutter and R. Snively, Witten diagrams revisited: the AdS geometry of conformal blocks, JHEP 01 (2016) 146 [arXiv:1508.00501] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    L.F. Alday and A. Bissi, Unitarity and positivity constraints for CFT at large central charge, JHEP 07 (2017) 044 [arXiv:1606.09593] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    L.F. Alday, A. Bissi and T. Lukowski, Lessons from crossing symmetry at large N , JHEP 06 (2015) 074 [arXiv:1410.4717] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    S. Caron-Huot, Analyticity in spin in conformal theories, JHEP 09 (2017) 078 [arXiv:1703.00278] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    N. Afkhami-Jeddi, T. Hartman, S. Kundu and A. Tajdini, Einstein gravity 3-point functions from conformal field theory, JHEP 12 (2017) 049 [arXiv:1610.09378] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    M. Kulaxizi, A. Parnachev and A. Zhiboedov, Bulk Phase Shift, CFT Regge Limit and Einstein Gravity, JHEP 06 (2018) 121 [arXiv:1705.02934] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    M.S. Costa, T. Hansen and J. Penedones, Bounds for OPE coefficients on the Regge trajectory, JHEP 10 (2017) 197 [arXiv:1707.07689] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    N. Afkhami-Jeddi, T. Hartman, S. Kundu and A. Tajdini, Shockwaves from the operator product expansion, arXiv:1709.03597 [INSPIRE].
  46. [46]
    D. Meltzer and E. Perlmutter, Beyond a = c: gravitational couplings to matter and the stress tensor OPE, JHEP 07 (2018) 157 [arXiv:1712.04861] [INSPIRE].
  47. [47]
    N. Afkhami-Jeddi, S. Kundu and A. Tajdini, A conformal collider for holographic CFTs, JHEP 10 (2018) 156 [arXiv:1805.07393] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a higher spin symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].
  49. [49]
    N. Boulanger, D. Ponomarev, E.D. Skvortsov and M. Taronna, On the uniqueness of higher-spin symmetries in AdS and CFT, Int. J. Mod. Phys. A 28 (2013) 1350162 [arXiv:1305.5180] [INSPIRE].
  50. [50]
    T. Hartman, S. Jain and S. Kundu, Causality constraints in conformal field theory, JHEP 05 (2016) 099 [arXiv:1509.00014] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    V. Alba and K. Diab, Constraining conformal field theories with a higher spin symmetry in d<3 dimensions, JHEP 03 (2016) 044 [arXiv:1510.02535] [INSPIRE].
  52. [52]
    N. Arkani-Hamed and J. Maldacena, Cosmological collider physics, arXiv:1503.08043 [INSPIRE].
  53. [53]
    C. Cordova, J. Maldacena and G.J. Turiaci, Bounds on OPE coefficients from interference effects in the conformal collider, JHEP 11 (2017) 032 [arXiv:1710.03199] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  54. [54]
    K. Hinterbichler, A. Joyce and R.A. Rosen, Eikonal scattering and asymptotic superluminality of massless higher spin fields, Phys. Rev. D 97 (2018) 125019 [arXiv:1712.10021] [INSPIRE].
  55. [55]
    J. Bonifacio, K. Hinterbichler, A. Joyce and R.A. Rosen, Massive and massless spin-2 scattering and asymptotic superluminality, JHEP 06 (2018) 075 [arXiv:1712.10020] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  56. [56]
    M. Levy and J. Sucher, Eikonal approximation in quantum field theory, Phys. Rev. 186 (1969) 1656 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  57. [57]
    X.O. Camanho, G. Lucena Gómez and R. Rahman, Causality constraints on massive gravity, Phys. Rev. D 96 (2017) 084007 [arXiv:1610.02033] [INSPIRE].
  58. [58]
    J.D. Edelstein et al., Causality in 3D massive gravity theories, Phys. Rev. D 95 (2017) 104016 [arXiv:1602.03376] [INSPIRE].
  59. [59]
    G. ’t Hooft, Graviton dominance in ultrahigh-energy scattering, Phys. Lett. B 198 (1987) 61 [INSPIRE].
  60. [60]
    I.I. Shapiro, Fourth test of general relativity, Phys. Rev. Lett. 13 (1964) 789 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  61. [61]
    S. Gao and R.M. Wald, Theorems on gravitational time delay and related issues, Class. Quant. Grav. 17 (2000) 4999 [gr-qc/0007021] [INSPIRE].
  62. [62]
    M.S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning conformal correlators, JHEP 11 (2011) 071 [arXiv:1107.3554] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  63. [63]
    G. Tiktopoulos and S.B. Treiman, Relativistic eikonal approximation, Phys. Rev. D 3 (1971) 1037 [INSPIRE].
  64. [64]
    H. Cheng and T.T. Wu, Expanding protons: scattering at high-energies, MIT Press, Cambridge U.S.A. (1987).Google Scholar
  65. [65]
    D.N. Kabat, Validity of the Eikonal approximation, Comments Nucl. Part. Phys. 20 (1992) 325 [hep-th/9204103] [INSPIRE].
  66. [66]
    L.P.S. Singh and C.R. Hagen, Lagrangian formulation for arbitrary spin. 1. The boson case, Phys. Rev. D 9 (1974) 898 [INSPIRE].
  67. [67]
    L.P.S. Singh and C.R. Hagen, Lagrangian formulation for arbitrary spin. 2. The fermion case, Phys. Rev. D 9 (1974) 910 [INSPIRE].
  68. [68]
    Yu. M. Zinoviev, On massive high spin particles in AdS, hep-th/0108192 [INSPIRE].
  69. [69]
    R. Rahman, Interacting massive higher spin fields, AAT-3365735, PROQUEST-1826271451 (2009).Google Scholar
  70. [70]
    J. Bonifacio and K. Hinterbichler, Universal bound on the strong coupling scale of a gravitationally coupled massive spin-2 particle, Phys. Rev. D 98 (2018) 085006 [arXiv:1806.10607] [INSPIRE].
  71. [71]
    M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  72. [72]
    P. Kravchuk and D. Simmons-Duffin, Light-ray operators in conformal field theory, JHEP 11 (2018) 102 [arXiv:1805.00098] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  73. [73]
    S. Ferrara, A.F. Grillo, G. Parisi and R. Gatto, The shadow operator formalism for conformal algebra. Vacuum expectation values and operator products, Lett. Nuovo Cim. 4S2 (1972) 115 [INSPIRE].
  74. [74]
    D. Simmons-Duffin, Projectors, shadows and conformal blocks, JHEP 04 (2014) 146 [arXiv:1204.3894] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  75. [75]
    F.A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [INSPIRE].
  76. [76]
    B. Czech et al., A stereoscopic look into the bulk, JHEP 07 (2016) 129 [arXiv:1604.03110] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  77. [77]
    J. de Boer, F.M. Haehl, M.P. Heller and R.C. Myers, Entanglement, holography and causal diamonds, JHEP 08 (2016) 162 [arXiv:1606.03307] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  78. [78]
    R.C. Brower, J. Polchinski, M.J. Strassler and C.-I. Tan, The Pomeron and gauge/string duality, JHEP 12 (2007) 005 [hep-th/0603115] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  79. [79]
    T. Hartman, S. Jain and S. Kundu, A new spin on causality constraints, JHEP 10 (2016) 141 [arXiv:1601.07904] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  80. [80]
    D.M. Hofman et al., A proof of the conformal collider bounds, JHEP 06 (2016) 111 [arXiv:1603.03771] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  81. [81]
    T. Hartman, S. Kundu and A. Tajdini, Averaged null energy condition from causality, JHEP 07 (2017) 066 [arXiv:1610.05308] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  82. [82]
    D.M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].ADSCrossRefGoogle Scholar
  83. [83]
    T. Faulkner, R.G. Leigh, O. Parrikar and H. Wang, Modular Hamiltonians for deformed half-spaces and the averaged null energy condition, JHEP 09 (2016) 038 [arXiv:1605.08072] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  84. [84]
    D. Amati, M. Ciafaloni and G. Veneziano, Effective action and all order gravitational eikonal at Planckian energies, Nucl. Phys. B 403 (1993) 707 [INSPIRE].
  85. [85]
    D. Amati, M. Ciafaloni and G. Veneziano, Planckian scattering beyond the semiclassical approximation, Phys. Lett. B 289 (1992) 87 [INSPIRE].
  86. [86]
    D. Amati, M. Ciafaloni and G. Veneziano, Can space-time be probed below the string size?, Phys. Lett. B 216 (1989) 41 [INSPIRE].
  87. [87]
    D. Amati, M. Ciafaloni and G. Veneziano, Classical and quantum gravity effects from planckian energy superstring collisions, Int. J. Mod. Phys. A 3 (1988) 1615 [INSPIRE].
  88. [88]
    D. Amati, M. Ciafaloni and G. Veneziano, Superstring collisions at planckian energies, Phys. Lett. B 197 (1987) 81 [INSPIRE].
  89. [89]
    M. Taronna, Higher spins and string interactions, arXiv:1005.3061 [INSPIRE].
  90. [90]
    A. Sagnotti and M. Taronna, String lessons for higher-spin interactions, Nucl. Phys. B 842 (2011) 299 [arXiv:1006.5242] [INSPIRE].
  91. [91]
    G. D’Appollonio, P. Di Vecchia, R. Russo and G. Veneziano, Regge behavior saves String Theory from causality violations, JHEP 05 (2015) 144 [arXiv:1502.01254] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  92. [92]
    A. Higuchi, Forbidden mass range for spin-2 field theory in de Sitter space-time, Nucl. Phys. B 282 (1987) 397 [INSPIRE].
  93. [93]
    S. Deser and A. Waldron, Partial masslessness of higher spins in (A)dS, Nucl. Phys. B 607 (2001) 577 [hep-th/0103198] [INSPIRE].
  94. [94]
    D. Baumann, Primordial cosmology, PoS(TASI2017)009 [arXiv:1807.03098] [INSPIRE].
  95. [95]
    H. Lee, D. Baumann and G.L. Pimentel, Non-gaussianity as a particle detector, JHEP 12 (2016) 040 [arXiv:1607.03735] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  96. [96]
    K.N. Abazajian et al., Neutrino physics from the Cosmic Microwave Background and large scale structure, Astropart. Phys. 63 (2015) 66 [arXiv:1309.5383] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsCornell UniversityIthacaU.S.A.
  2. 2.Department of Physics and AstronomyJohns Hopkins UniversityBaltimoreU.S.A.

Personalised recommendations