Advertisement

Journal of High Energy Physics

, 2019:156 | Cite as

Higher spin supersymmetry at the cosmological collider: sculpting SUSY rilles in the CMB

  • Stephon Alexander
  • S. James GatesJr
  • Leah Jenks
  • K. Koutrolikos
  • Evan McDonoughEmail author
Open Access
Regular Article - Theoretical Physics
  • 38 Downloads

Abstract

We study the imprint of higher spin supermultiplets on cosmological correlators, namely the non-Gaussianity of the cosmic microwave background. Supersymmetry is used as a guide to introduce the contribution of fermionic higher spin particles, which have been neglected thus far in the literature. This necessarily introduces more than just a single additional fermionic superpartner, since the spectrum of massive, higher spin super- multiplets includes two propagating higher spin bosons and two propagating higher spin fermions, which all contribute to the three point function. As an example we consider the half-integer superspin Y = s + 1/2 supermultiplet, which includes particles of spin values j = s + 1, j = s + 1/2, j = s + 1/2 and j = s. We compute the curvature perturbation 3-point function for higher spin particle exchange and find that the known Ps(cos θ) angu- lar dependence is accompanied by superpartner contributions that scale as Ps+1(cos θ) and \( {\sum}_m{P}_s^m\left(\cos \theta \right) \), with Ps and \( {P}_s^m \) defined as the Legendre and Associated Legendre polynomials respectively. We also compute the tensor-scalar-scalar 3-point function, and find a complicated angular dependence as an integral over products of Legendre and associated Legendre polynomials.

Keywords

Cosmology of Theories beyond the SM Higher Spin Symmetry Supersym- metric Effective Theories 

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]
    Planck collaboration, Planck 2018 results. I. Overview and the cosmological legacy of Planck, arXiv:1807.06205 [INSPIRE].
  2. [2]
    D. Wands, K.A. Malik, D.H. Lyth and A.R. Liddle, A New approach to the evolution of cosmological perturbations on large scales, Phys. Rev.D 62 (2000) 043527 [astro-ph/0003278] [INSPIRE].
  3. [3]
    S. Weinberg, Adiabatic modes in cosmology, Phys. Rev.D 67 (2003) 123504 [astro-ph/0302326] [INSPIRE].
  4. [4]
    G.I. Rigopoulos and E.P.S. Shellard, The separate universe approach and the evolution of nonlinear superhorizon cosmological perturbations, Phys. Rev.D 68 (2003) 123518 [astro-ph/0306620] [INSPIRE].
  5. [5]
    D.H. Lyth, K.A. Malik and M. Sasaki, A General proof of the conservation of the curvature perturbation, JCAP05 (2005) 004 [astro-ph/0411220] [INSPIRE].
  6. [6]
    D. Langlois and F. Vernizzi, Conserved non-linear quantities in cosmology, Phys. Rev.D 72 (2005) 103501 [astro-ph/0509078] [INSPIRE].
  7. [7]
    V. Assassi, D. Baumann and D. Green, Symmetries and Loops in Inflation, JHEP02 (2013) 151 [arXiv:1210.7792] [INSPIRE].
  8. [8]
    L. Senatore and M. Zaldarriaga, The constancy of ζ in single-clock Inflation at all loops, JHEP09 (2013) 148 [arXiv:1210.6048] [INSPIRE].
  9. [9]
    X. Chen and Y. Wang, Quasi-Single Field Inflation and Non-Gaussianities, JCAP04 (2010) 027 [arXiv:0911.3380] [INSPIRE].
  10. [10]
    X. Chen and Y. Wang, Large non-Gaussianities with Intermediate Shapes from Quasi-Single Field Inflation, Phys. Rev.D 81 (2010) 063511 [arXiv:0909.0496] [INSPIRE].
  11. [11]
    X. Chen, M.H. Namjoo and Y. Wang, Quantum Primordial Standard Clocks, JCAP02 (2016) 013 [arXiv:1509.03930] [INSPIRE].
  12. [12]
    N. Arkani-Hamed and J. Maldacena, Cosmological Collider Physics, arXiv:1503.08043 [INSPIRE].
  13. [13]
    H. Lee, D. Baumann and G.L. Pimentel, Non-Gaussianity as a Particle Detector, JHEP12 (2016) 040 [arXiv:1607.03735] [INSPIRE].
  14. [14]
    E. Majorana, Relativistic theory of particles with arbitrary intrinsic angular momentum, Nuovo Cim.9 (1932) 335 [INSPIRE].
  15. [15]
    T. Noumi, T. Takeuchi and S. Zhou, String Regge trajectory on de Sitter space and implications to inflation, arXiv:1907.02535 [INSPIRE].
  16. [16]
    D. Lüst and E. Palti, A Note on String Excitations and the Higuchi Bound, arXiv:1907.04161 [INSPIRE].
  17. [17]
    D.J. Gross, Strings at superPlanckian energies: In search of the string symmetry, Phil. Trans. Roy. Soc. Lond.A 329 (1989) 401 [INSPIRE].
  18. [18]
    E. Witten, The search for higher symmetry in string theory, Phil. Trans. Roy. Soc. Lond.A 329 (1989) 349 [INSPIRE].
  19. [19]
    D.J. Gross and P.F. Mende, String Theory Beyond the Planck Scale, Nucl. Phys.B 303 (1988) 407 [INSPIRE].
  20. [20]
    E.S. Fradkin and M.A. Vasiliev, Candidate to the Role of Higher Spin Symmetry, Annals Phys.177 (1987) 63 [INSPIRE].
  21. [21]
    R. Haag, J.T. Lopuszanski and M. Sohnius, All Possible Generators of Supersymmetries of the s Matrix, Nucl. Phys.B 88 (1975) 257 [INSPIRE].
  22. [22]
    I.L. Buchbinder, S.J. Gates Jr. and K. Koutrolikos, Superfield continuous spin equations of motion, Phys. Lett.B 793 (2019) 445 [arXiv:1903.08631] [INSPIRE].
  23. [23]
    S.M. Kuzenko, A.G. Sibiryakov and V.V. Postnikov, Massless gauge superfields of higher half integer superspins, JETP Lett.57 (1993) 534 [INSPIRE].
  24. [24]
    S.M. Kuzenko and A.G. Sibiryakov, Massless gauge superfields of higher integer superspins, JETP Lett.57 (1993) 539 [INSPIRE].
  25. [25]
    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].
  26. [26]
    I.L. Buchbinder, S.M. Kuzenko and A.G. Sibiryakov, Quantization of higher spin superfields in the anti-de Sitter superspace, Phys. Lett.B 352 (1995) 29 [hep-th/9502148] [INSPIRE].
  27. [27]
    S.J. Gates Jr., S.M. Kuzenko and A.G. Sibiryakov, N = 2 supersymmetry of higher superspin massless theories, Phys. Lett.B 412 (1997) 59 [hep-th/9609141] [INSPIRE].
  28. [28]
    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].
  29. [29]
    S.J. Gates Jr. and S.M. Kuzenko, 4D, N = 1 higher spin gauge superfields and quantized twistors, JHEP10 (2005) 008 [hep-th/0506255] [INSPIRE].
  30. [30]
    S.J. Gates Jr. and K. Koutrolikos, On 4D, Ɲ = 1 massless gauge superfields of arbitrary superhelicity, JHEP06 (2014) 098 [arXiv:1310.7385] [INSPIRE].
  31. [31]
    I.L. Buchbinder and K. Koutrolikos, BRST Analysis of the Supersymmetric Higher Spin Field Models, JHEP12 (2015) 106 [arXiv:1510.06569] [INSPIRE].
  32. [32]
    S.J. Gates Jr. and K. Koutrolikos, From Diophantus to Supergravity and massless higher spin multiplets, JHEP11 (2017) 063 [arXiv:1707.00194] [INSPIRE].
  33. [33]
    D. Sorokin and M. Tsulaia, Supersymmetric Reducible Higher-Spin Multiplets in Various Dimensions, Nucl. Phys.B 929 (2018) 216 [arXiv:1801.04615] [INSPIRE].
  34. [34]
    Y.M. Zinoviev, Massive N = 1 supermultiplets with arbitrary superspins, Nucl. Phys.B 785 (2007) 98 [arXiv:0704.1535] [INSPIRE].
  35. [35]
    I.L. Buchbinder, M.V. Khabarov, T.V. Snegirev and Y.M. Zinoviev, Lagrangian formulation of the massive higher spin N = 1 supermultiplets in AdS 4space, Nucl. Phys.B 942 (2019) 1 [arXiv:1901.09637] [INSPIRE].
  36. [36]
    S.J. Gates Jr., S.M. Kuzenko and G. Tartaglino-Mazzucchelli, New massive supergravity multiplets, JHEP02 (2007) 052 [hep-th/0610333] [INSPIRE].
  37. [37]
    S.J. Gates Jr. and K. Koutrolikos, A dynamical theory for linearized massive superspin 3/2, JHEP03 (2014) 030 [arXiv:1310.7387] [INSPIRE].
  38. [38]
    C. Cheung, P. Creminelli, A.L. Fitzpatrick, J. Kaplan and L. Senatore, The Effective Field Theory of Inflation, JHEP03 (2008) 014 [arXiv:0709.0293] [INSPIRE].
  39. [39]
    E.A. Bergshoeff, D.Z. Freedman, R. Kallosh and A. Van Proeyen, Pure de Sitter Supergravity, Phys. Rev.D 92 (2015) 085040 [Erratum ibid.D 93 (2016) 069901] [arXiv:1507.08264] [INSPIRE].
  40. [40]
    R. Kallosh and T. Wrase, de Sitter Supergravity Model Building, Phys. Rev.D 92 (2015) 105010 [arXiv:1509.02137] [INSPIRE].
  41. [41]
    R. Kallosh, Matter-coupled de Sitter Supergravity, Theor. Math. Phys.187 (2016) 695 [arXiv:1509.02136] [INSPIRE].
  42. [42]
    L.V. Delacretaz, V. Gorbenko and L. Senatore, The Supersymmetric Effective Field Theory of Inflation, JHEP03 (2017) 063 [arXiv:1610.04227] [INSPIRE].
  43. [43]
    S.J. Gates Jr., M.T. Grisaru and S. Penati, Holomorphy, minimal homotopy and the 4-D, N = 1 supersymmetric Bardeen-Gross-Jackiw anomaly, Phys. Lett.B 481 (2000) 397 [hep-th/0002045] [INSPIRE].
  44. [44]
    S.J. Gates Jr., M.T. Grisaru, M.E. Knutt, S. Penati and H. Suzuki, Supersymmetric gauge anomaly with general homotopic paths, Nucl. Phys.B 596 (2001) 315 [hep-th/0009192] [INSPIRE].
  45. [45]
    S.J. Gates Jr., M.T. Grisaru, M.E. Knutt and S. Penati, The Superspace WZNW action for 4-D, N = 1 supersymmetric QCD, Phys. Lett.B 503 (2001) 349 [hep-ph/0012301] [INSPIRE].
  46. [46]
    M.B. Green and J.H. Schwarz, Anomaly Cancellation in Supersymmetric D = 10 Gauge Theory and Superstring Theory, Phys. Lett.149B (1984) 117 [INSPIRE].
  47. [47]
    E.A. Bergshoeff and M. de Roo, The Quartic Effective Action of the Heterotic String and Supersymmetry, Nucl. Phys.B 328 (1989) 439 [INSPIRE].
  48. [48]
    C. Vafa and E. Witten, A One loop test of string duality, Nucl. Phys.B 447 (1995) 261 [hep-th/9505053] [INSPIRE].
  49. [49]
    M.J. Duff, J.T. Liu and R. Minasian, Eleven-dimensional origin of string-string duality: A One loop test, Nucl. Phys.B 452 (1995) 261 [hep-th/9506126] [INSPIRE].
  50. [50]
    E. Witten, Five-brane effective action in M-theory, J. Geom. Phys.22 (1997) 103 [hep-th/9610234] [INSPIRE].
  51. [51]
    K. Peeters, P. Vanhove and A. Westerberg, Supersymmetric higher derivative actions in ten-dimensions and eleven-dimensions, the associated superalgebras and their formulation in superspace, Class. Quant. Grav.18 (2001) 843 [hep-th/0010167] [INSPIRE].
  52. [52]
    M.B. Green and M. Gutperle, Effects of D instantons, Nucl. Phys.B 498 (1997) 195 [hep-th/9701093] [INSPIRE].
  53. [53]
    J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE].
  54. [54]
    D. Baumann and L. McAllister, Inflation and String Theory, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2015) [arXiv:1404.2601] [INSPIRE].
  55. [55]
    S.H.S. Alexander, Inflation from D − \( \overline{D} \)brane annihilation, Phys. Rev.D 65 (2002) 023507 [hep-th/0105032] [INSPIRE].
  56. [56]
    L. Randall and R. Sundrum, Out of this world supersymmetry breaking, Nucl. Phys.B 557 (1999) 79 [hep-th/9810155] [INSPIRE].
  57. [57]
    E. McDonough and M. Scalisi, Inflation from Nilpotent Kähler Corrections, JCAP11 (2016) 028 [arXiv:1609.00364] [INSPIRE].
  58. [58]
    R. Kallosh, A. Linde, D. Roest and Y. Yamada, \( \overline{D3} \)induced geometric inflation, JHEP07 (2017) 057 [arXiv:1705.09247] [INSPIRE].
  59. [59]
    S. Ferrara, R. Kallosh and A. Linde, Cosmology with Nilpotent Superfields, JHEP10 (2014) 143 [arXiv:1408.4096] [INSPIRE].
  60. [60]
    R. Kallosh and A. Linde, Inflation and Uplifting with Nilpotent Superfields, JCAP01 (2015) 025 [arXiv:1408.5950] [INSPIRE].
  61. [61]
    R.H. Brandenberger, Lectures on the theory of cosmological perturbations, Lect. Notes Phys.646 (2004) 127 [hep-th/0306071] [INSPIRE].
  62. [62]
    T. Curtright, Massless Field Supermultiplets With Arbitrary Spin, Phys. Lett.85B (1979) 219 [INSPIRE].
  63. [63]
    M.A. Vasiliev, ‘Gauge’ form of description of massless fields with arbitrary spin (in Russian), Yad. Fiz.32 (1980) 855 [INSPIRE].
  64. [64]
    S.J. Gates Jr., M.T. Grisaru, M. Roček and W. Siegel, Superspace Or One Thousand and One Lessons in Supersymmetry, Front. Phys.58 (1983) 1 [hep-th/0108200] [INSPIRE].
  65. [65]
    I.L. Buchbinder and S.M. Kuzenko, Ideas and methods of supersymmetry and supergravity: Or a walk through superspace, IOP (1998) [INSPIRE].
  66. [66]
    A. Higuchi, Forbidden Mass Range for Spin-2 Field Theory in de Sitter Space-time, Nucl. Phys.B 282(1987) 397 [INSPIRE].
  67. [67]
    S. Deser and A. Waldron, Partial masslessness of higher spins in (A)dS, Nucl. Phys.B 607 (2001) 577 [hep-th/0103198] [INSPIRE].
  68. [68]
    S.M. Kuzenko, R. Manvelyan and S. Theisen, Off-shell superconformal higher spin multiplets in four dimensions, JHEP07 (2017) 034 [arXiv:1701.00682] [INSPIRE].
  69. [69]
    I.L. Buchbinder, S.J. Gates Jr. and K. Koutrolikos, Higher Spin Superfield interactions with the Chiral Supermultiplet: Conserved Supercurrents and Cubic Vertices, Universe4 (2018) 6 [arXiv:1708.06262] [INSPIRE].
  70. [70]
    J. Hutomo and S.M. Kuzenko, Non-conformal higher spin supercurrents, Phys. Lett.B 778 (2018) 242 [arXiv:1710.10837] [INSPIRE].
  71. [71]
    K. Koutrolikos, P. KočÍ and R. von Unge, Higher Spin Superfield interactions with Complex linear Supermultiplet: Conserved Supercurrents and Cubic Vertices, JHEP03 (2018) 119 [arXiv:1712.05150] [INSPIRE].
  72. [72]
    I.L. Buchbinder, S.J. Gates Jr. and K. Koutrolikos, Interaction of supersymmetric nonlinear σ-models with external higher spin superfields via higher spin supercurrents, JHEP05 (2018) 204 [arXiv:1804.08539] [INSPIRE].
  73. [73]
    I.L. Buchbinder, S.J. Gates Jr. and K. Koutrolikos, Conserved higher spin supercurrents for arbitrary spin massless supermultiplets and higher spin superfield cubic interactions, JHEP08 (2018) 055 [arXiv:1805.04413] [INSPIRE].
  74. [74]
    E.I. Buchbinder, J. Hutomo and S.M. Kuzenko, Higher spin supercurrents in anti-de Sitter space, JHEP09 (2018) 027 [arXiv:1805.08055] [INSPIRE].
  75. [75]
    I.L. Buchbinder, S.J. Gates Jr. and K. Koutrolikos, Integer superspin supercurrents of matter supermultiplets, JHEP05 (2019) 031 [arXiv:1811.12858] [INSPIRE].
  76. [76]
    S.J. Gates and K. Koutrolikos, Progress on cubic interactions of arbitrary superspin supermultiplets via gauge invariant supercurrents, arXiv:1904.13336 [INSPIRE].
  77. [77]
    J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP05 (2003) 013 [astro-ph/0210603] [INSPIRE].
  78. [78]
    X. Chen, Primordial Non-Gaussianities from Inflation Models, Adv. Astron.2010 (2010) 638979 [arXiv:1002.1416] [INSPIRE].
  79. [79]
    P. Adshead, R. Easther and E.A. Lim, The ‘in-in’ Formalism and Cosmological Perturbations, Phys. Rev.D 80 (2009) 083521 [arXiv:0904.4207] [INSPIRE].
  80. [80]
    Y. Wang, Inflation, Cosmic Perturbations and Non-Gaussianities, Commun. Theor. Phys.62 (2014) 109 [arXiv:1303.1523] [INSPIRE].
  81. [81]
    A. Altland and B.D. Simons, Condensed Matter Field Theory, 2 edition, Cambridge University Press (2010).Google Scholar
  82. [82]
    E. Komatsu and D.N. Spergel, Acoustic signatures in the primary microwave background bispectrum, Phys. Rev.D 63 (2001) 063002 [astro-ph/0005036] [INSPIRE].
  83. [83]
    D. Baumann, G. Goon, H. Lee and G.L. Pimentel, Partially Massless Fields During Inflation, JHEP04 (2018) 140 [arXiv:1712.06624] [INSPIRE].
  84. [84]
    CMB-S4 collaboration, CMB-S4 Science Book, First Edition, arXiv:1610.02743 [INSPIRE].
  85. [85]
    H. Lee, High-Energy Aspects of Inflationary Cosmology, Ph.D. Thesis, Cambridge U., DAMTP (2017) [ https://doi.org/10.17863/CAM.20391].
  86. [86]
    D.H. Lyth and D. Roberts, Cosmological consequences of particle creation during inflation, Phys. Rev.D 57 (1998) 7120 [hep-ph/9609441] [INSPIRE].
  87. [87]
    N. Bartolo, A. Kehagias, M. Liguori, A. Riotto, M. Shiraishi and V. Tansella, Detecting higher spin fields through statistical anisotropy in the CMB and galaxy power spectra, Phys. Rev.D 97 (2018) 023503 [arXiv:1709.05695] [INSPIRE].
  88. [88]
    A. Moradinezhad Dizgah, G. Franciolini, A. Kehagias and A. Riotto, Constraints on long-lived, higher-spin particles from galaxy bispectrum, Phys. Rev.D 98 (2018) 063520 [arXiv:1805.10247] [INSPIRE].
  89. [89]
    A. Moradinezhad Dizgah and C. Dvorkin, Scale-Dependent Galaxy Bias from Massive Particles with Spin during Inflation, JCAP01 (2018) 010 [arXiv:1708.06473] [INSPIRE].
  90. [90]
    A. Moradinezhad Dizgah, H. Lee, J.B. Muñoz and C. Dvorkin, Galaxy Bispectrum from Massive Spinning Particles, JCAP05 (2018) 013 [arXiv:1801.07265] [INSPIRE].
  91. [91]
    L. Bordin and G. Cabass, Probing higher-spin fields from inflation with higher-order statistics of the CMB, JCAP06 (2019) 050 [arXiv:1902.09519] [INSPIRE].
  92. [92]
    K. Kogai, T. Matsubara, A.J. Nishizawa and Y. Urakawa, Intrinsic galaxy alignment from angular dependent primordial non-Gaussianity, JCAP08 (2018) 014 [arXiv:1804.06284] [INSPIRE].
  93. [93]
    A. Kehagias and A. Riotto, On the Inflationary Perturbations of Massive Higher-Spin Fields, JCAP07 (2017) 046 [arXiv:1705.05834] [INSPIRE].
  94. [94]
    G. Franciolini, A. Kehagias and A. Riotto, Imprints of Spinning Particles on Primordial Cosmological Perturbations, JCAP02 (2018) 023 [arXiv:1712.06626] [INSPIRE].
  95. [95]
    G. Franciolini, A. Kehagias, A. Riotto and M. Shiraishi, Detecting higher spin fields through statistical anisotropy in the CMB bispectrum, Phys. Rev.D 98 (2018) 043533 [arXiv:1803.03814] [INSPIRE].
  96. [96]
    D. Marolf, L. Martucci and P.J. Silva, Actions and Fermionic symmetries for D-branes in bosonic backgrounds, JHEP07 (2003) 019 [hep-th/0306066] [INSPIRE].
  97. [97]
    D. Marolf, L. Martucci and P.J. Silva, Fermions, T duality and effective actions for D-branes in bosonic backgrounds, JHEP04 (2003) 051 [hep-th/0303209] [INSPIRE].
  98. [98]
    L. Martucci, J. Rosseel, D. Van den Bleeken and A. Van Proeyen, Dirac actions for D-branes on backgrounds with fluxes, Class. Quant. Grav.22 (2005) 2745 [hep-th/0504041] [INSPIRE].
  99. [99]
    K. Dasgupta, M. Emelin and E. McDonough, Fermions on the antibrane: Higher order interactions and spontaneously broken supersymmetry, Phys. Rev.D 95 (2017) 026003 [arXiv:1601.03409] [INSPIRE].
  100. [100]
    X. Chen, H. Firouzjahi, M.H. Namjoo and M. Sasaki, A Single Field Inflation Model with Large Local Non-Gaussianity, EPL102 (2013) 59001 [arXiv:1301.5699] [INSPIRE].
  101. [101]
    R. Holman and A.J. Tolley, Enhanced Non-Gaussianity from Excited Initial States, JCAP05 (2008) 001 [arXiv:0710.1302] [INSPIRE].
  102. [102]
    N. Arkani-Hamed, D. Baumann, H. Lee and G.L. Pimentel, The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities, arXiv:1811.00024 [INSPIRE].
  103. [103]
    E. Witten, String theory dynamics in various dimensions, Nucl. Phys.B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
  104. [104]
    P. Hořava and E. Witten, Heterotic and type-I string dynamics from eleven-dimensions, Nucl. Phys.B 460 (1996) 506 [hep-th/9510209] [INSPIRE].
  105. [105]
    C. Hull and B. Zwiebach, Double Field Theory, JHEP09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
  106. [106]
    P.D. Meerburg, J. Meyers, A. van Engelen and Y. Ali-Häımoud, CMB B-mode non-Gaussianity, Phys. Rev.D 93 (2016) 123511 [arXiv:1603.02243] [INSPIRE].
  107. [107]
    S.J. Gates Jr., Sticking with SUSY, Phys. World27 (2014) 32.Google Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Stephon Alexander
    • 1
    • 2
  • S. James GatesJr
    • 1
    • 2
  • Leah Jenks
    • 1
  • K. Koutrolikos
    • 1
  • Evan McDonough
    • 1
    Email author
  1. 1.Department of PhysicsBrown UniversityProvidenceU.S.A.
  2. 2.Brown Theoretical Physics CenterProvidenceU.S.A.

Personalised recommendations