Journal of High Energy Physics

, 2013:121 | Cite as

Dynamics of a stabilized radion and duality

  • Zackaria Chacko
  • Rashmish K. Mishra
  • Daniel Stolarski


We construct the effective theory of the graviscalar radion in the Randall-Sundrum scenario, taking into account effects arising from the stabilization of the extra dimension through the Goldberger-Wise mechanism. We explore the conditions under which the radion can remain light, and determine the corrections to its couplings to Standard Model (SM) states when the effects of stabilization are taken into account. We show that in the theories of interest for electroweak symmetry breaking that have a holographic dual, the presence of a light radion in the spectrum is not a robust prediction of the framework, but is in fact associated with mild tuning. We find that corrections to the form of the radion couplings to Standard Model particles arising from effects associated with brane stabilization are suppressed by the square of the ratio of the radion mass to the Kaluza-Klein scale. These corrections are small in theories where the radion is light, and are generally subleading, except in the case of couplings to the SM gluons and photon, when they can sometimes dominate. The AdS/CFT correspondence relates the radion in Randall-Sundrum models to the dilaton in theories where a strongly coupled conformal symmetry is spontaneously broken. We show that the discrepancies in the literature between the results for the dilaton and the radion can be traced to the omission of self-interaction terms that would otherwise dominate the potential for the Goldberger-Wise scalar near the infrared brane. In the dual picture, this corresponds to neglecting the corrections to the scaling behavior of the operator that breaks conformal symmetry when it grows large. With the inclusion of these self-interaction terms, we find good agreement between the results on the two sides of the correspondence.


AdS-CFT Correspondence Field Theories in Higher Dimensions Beyond Standard Model Conformal and W Symmetry 


  1. [1]
    CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].ADSGoogle Scholar
  2. [2]
    ATLAS collaboration, Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].ADSGoogle Scholar
  3. [3]
    L. Susskind, Dynamics of spontaneous symmetry breaking in the Weinberg-Salam theory, Phys. Rev. D 20 (1979) 2619 [INSPIRE].ADSGoogle Scholar
  4. [4]
    G. ’t Hooft et al., Recent developments in gauge theories. Proceedings, Nato Advanced Study Institute, Cargese, France, August 26-September 8, 1979, NATO Adv. Study Inst. B 59 (1980) 1.Google Scholar
  5. [5]
    L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  6. [6]
    K. Agashe, A. Delgado, M.J. May and R. Sundrum, RS1, custodial isospin and precision tests, JHEP 08 (2003) 050 [hep-ph/0308036] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    K. Agashe, R. Contino, L. Da Rold and A. Pomarol, A custodial symmetry for Zbb, Phys. Lett. B 641 (2006) 62 [hep-ph/0605341] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    C. Csáki, C. Grojean, L. Pilo and J. Terning, Towards a realistic model of Higgsless electroweak symmetry breaking, Phys. Rev. Lett. 92 (2004) 101802 [hep-ph/0308038] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    R. Contino, Y. Nomura and A. Pomarol, Higgs as a holographic pseudoGoldstone boson, Nucl. Phys. B 671 (2003) 148 [hep-ph/0306259] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    K. Agashe, R. Contino and A. Pomarol, The minimal composite Higgs model, Nucl. Phys. B 719 (2005) 165 [hep-ph/0412089] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    Y. Grossman and M. Neubert, Neutrino masses and mixings in nonfactorizable geometry, Phys. Lett. B 474 (2000) 361 [hep-ph/9912408] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    T. Gherghetta and A. Pomarol, Bulk fields and supersymmetry in a slice of AdS, Nucl. Phys. B 586 (2000) 141 [hep-ph/0003129] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    K. Agashe, G. Perez and A. Soni, Flavor structure of warped extra dimension models, Phys. Rev. D 71 (2005) 016002 [hep-ph/0408134] [INSPIRE].ADSGoogle Scholar
  14. [14]
    K. Agashe and G. Servant, Warped unification, proton stability and dark matter, Phys. Rev. Lett. 93 (2004) 231805 [hep-ph/0403143] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    K. Agashe and G. Servant, Baryon number in warped GUTs: model building and (dark matter related) phenomenology, JCAP 02 (2005) 002 [hep-ph/0411254] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    A.D. Medina and E. Ponton, Warped radion dark matter, JHEP 09 (2011) 016 [arXiv:1104.4124] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    K. Agashe, A. Belyaev, T. Krupovnickas, G. Perez and J. Virzi, LHC signals from warped extra dimensions, Phys. Rev. D 77 (2008) 015003 [hep-ph/0612015] [INSPIRE].ADSGoogle Scholar
  18. [18]
    R. Contino, T. Kramer, M. Son and R. Sundrum, Warped/composite phenomenology simplified, JHEP 05 (2007) 074 [hep-ph/0612180] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    B. Lillie, L. Randall and L.-T. Wang, The bulk RS KK-gluon at the LHC, JHEP 09 (2007) 074 [hep-ph/0701166] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    C. Csáki, M. Graesser, L. Randall and J. Terning, Cosmology of brane models with radion stabilization, Phys. Rev. D 62 (2000) 045015 [hep-ph/9911406] [INSPIRE].ADSGoogle Scholar
  22. [22]
    W.D. Goldberger and M.B. Wise, Phenomenology of a stabilized modulus, Phys. Lett. B 475 (2000) 275 [hep-ph/9911457] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    G.F. Giudice, R. Rattazzi and J.D. Wells, Graviscalars from higher dimensional metrics and curvature Higgs mixing, Nucl. Phys. B 595 (2001) 250 [hep-ph/0002178] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    C. Csáki, M.L. Graesser and G.D. Kribs, Radion dynamics and electroweak physics, Phys. Rev. D 63 (2001) 065002 [hep-th/0008151] [INSPIRE].ADSGoogle Scholar
  25. [25]
    C. Csáki, J. Hubisz and S.J. Lee, Radion phenomenology in realistic warped space models, Phys. Rev. D 76 (2007) 125015 [arXiv:0705.3844] [INSPIRE].ADSGoogle Scholar
  26. [26]
    T.G. Rizzo, Radion couplings to bulk fields in the Randall-Sundrum model, JHEP 06 (2002) 056 [hep-ph/0205242] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
  28. [28]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].MathSciNetADSMATHGoogle Scholar
  29. [29]
    S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  30. [30]
    I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    N. Arkani-Hamed, M. Porrati and L. Randall, Holography and phenomenology, JHEP 08 (2001) 017 [hep-th/0012148] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    R. Rattazzi and A. Zaffaroni, Comments on the holographic picture of the Randall-Sundrum model, JHEP 04 (2001) 021 [hep-th/0012248] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  33. [33]
    A. Salam and J. Strathdee, Nonlinear realizations. 2. Conformal symmetry, Phys. Rev. 184 (1969) 1760 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  34. [34]
    C. Isham, A. Salam and J. Strathdee, Spontaneous breakdown of conformal symmetry, Phys. Lett. B 31 (1970) 300 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  35. [35]
    C. Isham, A. Salam and J. Strathdee, Nonlinear realizations of space-time symmetries. Scalar and tensor gravity, Annals Phys. 62 (1971) 98 [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  36. [36]
    B. Zumino, Lectures on elementary particles and quantum field theory, in 1970 Brandeis Summer School, S. Deser ed., MIT Press, U.S.A. (1970).Google Scholar
  37. [37]
    J.R. Ellis, Aspects of conformal symmetry and chirality, Nucl. Phys. B 22 (1970) 478 [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    J.R. Ellis, Phenomenological actions for spontaneously-broken conformal symmetry, Nucl. Phys. B 26 (1971) 536 [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    W.D. Goldberger, B. Grinstein and W. Skiba, Distinguishing the Higgs boson from the dilaton at the Large Hadron Collider, Phys. Rev. Lett. 100 (2008) 111802 [arXiv:0708.1463] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    J. Fan, W.D. Goldberger, A. Ross and W. Skiba, Standard Model couplings and collider signatures of a light scalar, Phys. Rev. D 79 (2009) 035017 [arXiv:0803.2040] [INSPIRE].ADSGoogle Scholar
  41. [41]
    L. Vecchi, Phenomenology of a light scalar: the dilaton, Phys. Rev. D 82 (2010) 076009 [arXiv:1002.1721] [INSPIRE].ADSGoogle Scholar
  42. [42]
    R. Rattazzi, The naturally light dilaton, talk given at Planck 2010. rom the Planck Scale to the ElectroWeak Scale, May 01-June 3, Lisbon, Portugal (2010).Google Scholar
  43. [43]
    Z. Chacko and R.K. Mishra, Effective theory of a light dilaton, Phys. Rev. D 87 (2013) 115006 [arXiv:1209.3022] [INSPIRE].ADSGoogle Scholar
  44. [44]
    B. Bellazzini, C. Csáki, J. Hubisz, J. Serra and J. Terning, A Higgslike dilaton, Eur. Phys. J. C 73 (2013) 2333 [arXiv:1209.3299] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    T. Abe et al., Minimal dilaton model, Phys. Rev. D 86 (2012) 115016 [arXiv:1209.4544] [INSPIRE].ADSGoogle Scholar
  46. [46]
    F. Coradeschi, P. Lodone, D. Pappadopulo, R. Rattazzi and L. Vitale, A naturally light dilaton, arXiv:1306.4601 [INSPIRE].
  47. [47]
    C. Charmousis, R. Gregory and V. Rubakov, Wave function of the radion in a brane world, Phys. Rev. D 62 (2000) 067505 [hep-th/9912160] [INSPIRE].MathSciNetADSGoogle Scholar
  48. [48]
    M.A. Luty and R. Sundrum, Hierarchy stabilization in warped supersymmetry, Phys. Rev. D 64 (2001) 065012 [hep-th/0012158] [INSPIRE].MathSciNetADSGoogle Scholar
  49. [49]
    P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  50. [50]
    C.M. Bender and S.A. Orszag, Advanced mathematical methods for scientists and engineers, McGraw-Hill Publishing Company, U.S.A. (1978).MATHGoogle Scholar
  51. [51]
    T. Konstandin, G. Nardini and M. Quirós, Gravitational backreaction effects on the holographic phase transition, Phys. Rev. D 82 (2010) 083513 [arXiv:1007.1468] [INSPIRE].ADSGoogle Scholar
  52. [52]
    Y. Eshel, S.J. Lee, G. Perez and Y. Soreq, Shining flavor and radion phenomenology in warped extra dimension, JHEP 10 (2011) 015 [arXiv:1106.6218] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    H. Georgi and A. Pais, Calculability and naturalness in gauge theories, Phys. Rev. D 10 (1974) 539 [INSPIRE].ADSGoogle Scholar
  54. [54]
    H. Georgi and A. Pais, Vacuum symmetry and the pseudogoldstone phenomenon, Phys. Rev. D 12 (1975) 508 [INSPIRE].ADSGoogle Scholar
  55. [55]
    D.B. Kaplan and H. Georgi, SU(2) × U(1) breaking by vacuum misalignment, Phys. Lett. B 136 (1984) 183 [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    D.B. Kaplan, H. Georgi and S. Dimopoulos, Composite Higgs scalars, Phys. Lett. B 136 (1984) 187 [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    H. Georgi and D.B. Kaplan, Composite Higgs and custodial SU(2), Phys. Lett. B 145 (1984) 216 [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    C. Arzt, Reduced effective lagrangians, Phys. Lett. B 342 (1995) 189 [hep-ph/9304230] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    H. Georgi, On-shell effective field theory, Nucl. Phys. B 361 (1991) 339 [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    M. Porrati and A. Starinets, RG fixed points in supergravity duals of 4D field theory and asymptotically AdS spaces, Phys. Lett. B 454 (1999) 77 [hep-th/9903085] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  61. [61]
    V. Balasubramanian and P. Kraus, Space-time and the holographic renormalization group, Phys. Rev. Lett. 83 (1999) 3605 [hep-th/9903190] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  62. [62]
    H.L. Verlinde, Holography and compactification, Nucl. Phys. B 580 (2000) 264 [hep-th/9906182] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  63. [63]
    J. de Boer, E.P. Verlinde and H.L. Verlinde, On the holographic renormalization group, JHEP 08 (2000) 003 [hep-th/9912012] [INSPIRE].CrossRefGoogle Scholar
  64. [64]
    E.P. Verlinde and H.L. Verlinde, RG flow, gravity and the cosmological constant, JHEP 05 (2000) 034 [hep-th/9912018] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  65. [65]
    V. Balasubramanian, E.G. Gimon and D. Minic, Consistency conditions for holographic duality, JHEP 05 (2000) 014 [hep-th/0003147] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  66. [66]
    S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  67. [67]
    A. Manohar and H. Georgi, Chiral quarks and the nonrelativistic quark model, Nucl. Phys. B 234 (1984) 189 [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    H. Georgi and L. Randall, Flavor conserving CP-violation in invisible axion models, Nucl. Phys. B 276 (1986) 241 [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    Z. Chacko, M.A. Luty and E. Ponton, Massive higher dimensional gauge fields as messengers of supersymmetry breaking, JHEP 07 (2000) 036 [hep-ph/9909248] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • Zackaria Chacko
    • 1
  • Rashmish K. Mishra
    • 1
  • Daniel Stolarski
    • 1
    • 2
  1. 1.Maryland Center for Fundamental Physics, Department of PhysicsUniversity of MarylandCollege ParkU.S.A.
  2. 2.Department of Physics and AstronomyJohns Hopkins UniversityBaltimoreU.S.A.

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