Probing the holographic dilaton

Abstract

Many strongly coupled field theories admit a spectrum of gauge-invariant bound states that includes scalar particles with the same quantum numbers as the vacuum. The challenge naturally arises of how to characterise them. In particular, how can a dilaton — the pseudo-Nambu-Goldstone boson associated with approximate scale invariance — be distinguished from other generic light scalars with the same quantum numbers? We address this problem within the context of gauge-gravity dualities, by analysing the fluctuations of the higher-dimensional gravitational theory. The diagnostic test that we propose consists of comparing the results of the complete calculation, performed by using gauge-invariant fluctuations in the bulk, with the results obtained in the probe approximation. While the former captures the mixing between scalar and metric degrees of freedom, the latter removes by hand the fluctuations that source the dilatation operator of the boundary field- theory. Hence, the probe approximation cannot capture a possible light dilaton, while it should fare well for other scalar particles. We test this idea on a number of holographic models, among which are some of the best known, complete gravity backgrounds constructed within the top-down approach to gauge-gravity dualities. We compute the spectra of scalar and tensor fluctuations, that are interpreted as bound states (glueballs) of the dual field theory, and we highlight those cases in which the probe approximation yields results close to the correct physical ones, as well as those cases where significant discrepancies emerge. We interpret the latter occurrence as an indication that identifying one of the lightest scalar states with the dilaton is legitimate, at least as a leading-order approximation.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    S. Coleman, Aspects of Symmetry: Selected Erice Lectures, Cambridge University Press (1985) [INSPIRE].

  2. [2]

    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].

  3. [3]

    D.K. Hong, S.D.H. Hsu and F. Sannino, Composite Higgs from higher representations, Phys. Lett. B597 (2004) 89 [hep-ph/0406200] [INSPIRE].

  4. [4]

    D.D. Dietrich, F. Sannino and K. Tuominen, Light composite Higgs from higher representations versus electroweak precision measurements: Predictions for CERN LHC, Phys. Rev. D72 (2005) 055001 [hep-ph/0505059] [INSPIRE].

  5. [5]

    M. Hashimoto and K. Yamawaki, Techni-dilaton at Conformal Edge, Phys. Rev. D83 (2011) 015008 [arXiv:1009.5482] [INSPIRE].

  6. [6]

    T. Appelquist and Y. Bai, A Light Dilaton in Walking Gauge Theories, Phys. Rev. D82 (2010) 071701 [arXiv:1006.4375] [INSPIRE].

  7. [7]

    L. Vecchi, Phenomenology of a light scalar: the dilaton, Phys. Rev. D82 (2010) 076009 [arXiv:1002.1721] [INSPIRE].

  8. [8]

    Z. Chacko and R.K. Mishra, Effective Theory of a Light Dilaton, Phys. Rev. D87 (2013) 115006 [arXiv:1209.3022] [INSPIRE].

  9. [9]

    B. Bellazzini, C. Csáki, J. Hubisz, J. Serra and J. Terning, A Higgslike Dilaton, Eur. Phys. J. C73 (2013) 2333 [arXiv:1209.3299] [INSPIRE].

  10. [10]

    T. Abe, R. Kitano, Y. Konishi, K.-y. Oda, J. Sato and S. Sugiyama, Minimal Dilaton Model, Phys. Rev. D86 (2012) 115016 [arXiv:1209.4544] [INSPIRE].

  11. [11]

    E. Eichten, K. Lane and A. Martin, A Higgs Impostor in Low-Scale Technicolor, arXiv:1210.5462 [INSPIRE].

  12. [12]

    P. Hernández-Leon and L. Merlo, Distinguishing A Higgs-Like Dilaton Scenario With A Complete Bosonic Effective Field Theory Basis, Phys. Rev. D96 (2017) 075008 [arXiv:1703.02064] [INSPIRE].

  13. [13]

    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. B716 (2012) 1 [arXiv:1207.7214] [INSPIRE].

  14. [14]

    CMS collaboration, Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC, Phys. Lett. B716 (2012) 30 [arXiv:1207.7235] [INSPIRE].

  15. [15]

    C.N. Leung, S.T. Love and W.A. Bardeen, Spontaneous Symmetry Breaking in Scale Invariant Quantum Electrodynamics, Nucl. Phys. B273 (1986) 649 [INSPIRE].

  16. [16]

    W.A. Bardeen, C.N. Leung and S.T. Love, The Dilaton and Chiral Symmetry Breaking, Phys. Rev. Lett.56 (1986) 1230 [INSPIRE].

  17. [17]

    K. Yamawaki, M. Bando and K.-i. Matumoto, Scale Invariant Technicolor Model and a Technidilaton, Phys. Rev. Lett.56 (1986) 1335 [INSPIRE].

  18. [18]

    LatKMI collaboration, Light composite scalar in eight-flavor QCD on the lattice, Phys. Rev. D89 (2014) 111502 [arXiv:1403.5000] [INSPIRE].

  19. [19]

    T. Appelquist et al., Strongly interacting dynamics and the search for new physics at the LHC, Phys. Rev. D93 (2016) 114514 [arXiv:1601.04027] [INSPIRE].

  20. [20]

    LatKMI collaboration, Light flavor-singlet scalars and walking signals in Nf = 8 QCD on the lattice, Phys. Rev. D96 (2017) 014508 [arXiv:1610.07011] [INSPIRE].

  21. [21]

    A.D. Gasbarro and G.T. Fleming, Examining the Low Energy Dynamics of Walking Gauge Theory, PoSLATTICE2016 (2017) 242 [arXiv:1702.00480] [INSPIRE].

  22. [22]

    Lattice Strong Dynamics collaboration, Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavors, Phys. Rev. D99 (2019) 014509 [arXiv:1807.08411] [INSPIRE].

  23. [23]

    Z. Fodor, K. Holland, J. Kuti, D. Nogradi, C. Schroeder and C.H. Wong, Can the nearly conformal sextet gauge model hide the Higgs impostor?, Phys. Lett. B718 (2012) 657 [arXiv:1209.0391] [INSPIRE].

  24. [24]

    Z. Fodor, K. Holland, J. Kuti, S. Mondal, D. Nogradi and C.H. Wong, Toward the minimal realization of a light composite Higgs, PoSLATTICE2014 (2015) 244 [arXiv:1502.00028] [INSPIRE].

  25. [25]

    Z. Fodor, K. Holland, J. Kuti, S. Mondal, D. Nogradi and C.H. Wong, Status of a minimal composite Higgs theory, PoSLATTICE2015 (2016) 219 [arXiv:1605.08750] [INSPIRE].

  26. [26]

    Z. Fodor, K. Holland, J. Kuti, D. Nogradi and C.H. Wong, The twelve-flavor β-function and dilaton tests of the sextet scalar, EPJ Web Conf.175 (2018) 08015 [arXiv:1712.08594] [INSPIRE].

  27. [27]

    Z. Fodor, K. Holland, J. Kuti and C.H. Wong, Tantalizing dilaton tests from a near-conformal EFT, PoSLATTICE2018 (2019) 196 [arXiv:1901.06324] [INSPIRE].

  28. [28]

    S. Matsuzaki and K. Yamawaki, Dilaton Chiral Perturbation Theory: Determining the Mass and Decay Constant of the Technidilaton on the Lattice, Phys. Rev. Lett.113 (2014) 082002 [arXiv:1311.3784] [INSPIRE].

  29. [29]

    M. Golterman and Y. Shamir, Low-energy effective action for pions and a dilatonic meson, Phys. Rev. D94 (2016) 054502 [arXiv:1603.04575] [INSPIRE].

  30. [30]

    A. Kasai, K.-i. Okumura and H. Suzuki, A dilaton-pion mass relation, arXiv:1609.02264 [INSPIRE].

  31. [31]

    M. Golterman and Y. Shamir, Effective action for pions and a dilatonic meson, PoSLATTICE2016 (2016) 205 [arXiv:1610.01752] [INSPIRE].

  32. [32]

    M. Hansen, K. Langæble and F. Sannino, Extending Chiral Perturbation Theory with an Isosinglet Scalar, Phys. Rev. D95 (2017) 036005 [arXiv:1610.02904] [INSPIRE].

  33. [33]

    M. Golterman and Y. Shamir, Effective pion mass term and the trace anomaly, Phys. Rev. D95 (2017) 016003 [arXiv:1611.04275] [INSPIRE].

  34. [34]

    T. Appelquist, J. Ingoldby and M. Piai, Dilaton EFT Framework For Lattice Data, JHEP07 (2017) 035 [arXiv:1702.04410] [INSPIRE].

  35. [35]

    T. Appelquist, J. Ingoldby and M. Piai, Analysis of a Dilaton EFT for Lattice Data, JHEP03 (2018) 039 [arXiv:1711.00067] [INSPIRE].

  36. [36]

    O. Catà, R.J. Crewther and L.C. Tunstall, Crawling technicolor, Phys. Rev. D100 (2019) 095007 [arXiv:1803.08513] [INSPIRE].

  37. [37]

    M. Golterman and Y. Shamir, Large-mass regime of the dilaton-pion low-energy effective theory, Phys. Rev. D98 (2018) 056025 [arXiv:1805.00198] [INSPIRE].

  38. [38]

    O. Catà and C. Müller, Chiral effective theories with a light scalar at one loop, Nucl. Phys. B952 (2020) 114938 [arXiv:1906.01879] [INSPIRE].

  39. [39]

    T. Appelquist, J. Ingoldby and M. Piai, Dilaton potential and lattice data, Phys. Rev. D101 (2020) 075025 [arXiv:1908.00895] [INSPIRE].

  40. [40]

    Z. Fodor, K. Holland, J. Kuti and C.H. Wong, Dilaton EFT from p-regime to RMT in the ϵ-regime, in 37th International Symposium on Lattice Field Theory, (2020) [arXiv:2002.05163] [INSPIRE].

  41. [41]

    M. Golterman, E.T. Neil and Y. Shamir, Application of dilaton chiral perturbation theory to Nf = 8, SU(3) spectral data, arXiv:2003.00114 [INSPIRE].

  42. [42]

    J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE].

  43. [43]

    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B428 (1998) 105 [hep-th/9802109] [INSPIRE].

  44. [44]

    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2 (1998) 253 [hep-th/9802150] [INSPIRE].

  45. [45]

    O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept.323 (2000) 183 [hep-th/9905111] [INSPIRE].

  46. [46]

    M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B631 (2002) 159 [hep-th/0112119] [INSPIRE].

  47. [47]

    K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav.19 (2002) 5849 [hep-th/0209067] [INSPIRE].

  48. [48]

    I. Papadimitriou and K. Skenderis, AdS/CFT correspondence and geometry, IRMA Lect. Math. Theor. Phys.8 (2005) 73 [hep-th/0404176] [INSPIRE].

  49. [49]

    W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett.83 (1999) 4922 [hep-ph/9907447] [INSPIRE].

  50. [50]

    O. DeWolfe, D.Z. Freedman, S.S. Gubser and A. Karch, Modeling the fifth-dimension with scalars and gravity, Phys. Rev. D62 (2000) 046008 [hep-th/9909134] [INSPIRE].

  51. [51]

    W.D. Goldberger and M.B. Wise, Phenomenology of a stabilized modulus, Phys. Lett. B475 (2000) 275 [hep-ph/9911457] [INSPIRE].

  52. [52]

    C. Csáki, M.L. Graesser and G.D. Kribs, Radion dynamics and electroweak physics, Phys. Rev. D63 (2001) 065002 [hep-th/0008151] [INSPIRE].

  53. [53]

    N. Arkani-Hamed, M. Porrati and L. Randall, Holography and phenomenology, JHEP08 (2001) 017 [hep-th/0012148] [INSPIRE].

  54. [54]

    R. Rattazzi and A. Zaffaroni, Comments on the holographic picture of the Randall-Sundrum model, JHEP04 (2001) 021 [hep-th/0012248] [INSPIRE].

  55. [55]

    L. Kofman, J. Martin and M. Peloso, Exact identification of the radion and its coupling to the observable sector, Phys. Rev. D70 (2004) 085015 [hep-ph/0401189] [INSPIRE].

  56. [56]

    D. Kutasov, J. Lin and A. Parnachev, Holographic Walking from Tachyon DBI, Nucl. Phys. B863 (2012) 361 [arXiv:1201.4123] [INSPIRE].

  57. [57]

    M. Goykhman and A. Parnachev, S-parameter, Technimesons and Phase Transitions in Holographic Tachyon DBI Models, Phys. Rev. D87 (2013) 026007 [arXiv:1211.0482] [INSPIRE].

  58. [58]

    N. Evans and K. Tuominen, Holographic modelling of a light technidilaton, Phys. Rev. D87 (2013) 086003 [arXiv:1302.4553] [INSPIRE].

  59. [59]

    E. Megias and O. Pujolàs, Naturally light dilatons from nearly marginal deformations, JHEP08 (2014) 081 [arXiv:1401.4998] [INSPIRE].

  60. [60]

    A. Pomarol, O. Pujolàs and L. Salas, Holographic conformal transition and light scalars, JHEP10 (2019) 202 [arXiv:1905.02653] [INSPIRE].

  61. [61]

    D. Elander, C. Núñez and M. Piai, A Light scalar from walking solutions in gauge-string duality, Phys. Lett. B686 (2010) 64 [arXiv:0908.2808] [INSPIRE].

  62. [62]

    D. Elander and M. Piai, A composite light scalar, electro-weak symmetry breaking and the recent LHC searches, Nucl. Phys. B864 (2012) 241 [arXiv:1112.2915] [INSPIRE].

  63. [63]

    D. Elander and M. Piai, The decay constant of the holographic techni-dilaton and the 125 GeV boson, Nucl. Phys. B867 (2013) 779 [arXiv:1208.0546] [INSPIRE].

  64. [64]

    D. Elander and M. Piai, On the glueball spectrum of walking backgrounds from wrapped-D5 gravity duals, Nucl. Phys. B871 (2013) 164 [arXiv:1212.2600] [INSPIRE].

  65. [65]

    D. Elander, Light scalar from deformations of the Klebanov-Strassler background, Phys. Rev. D91 (2015) 126012 [arXiv:1401.3412] [INSPIRE].

  66. [66]

    D. Elander, R. Lawrance and M. Piai, Hyperscaling violation and Electroweak Symmetry Breaking, Nucl. Phys. B897 (2015) 583 [arXiv:1504.07949] [INSPIRE].

  67. [67]

    D. Elander and M. Piai, Calculable mass hierarchies and a light dilaton from gravity duals, Phys. Lett. B772 (2017) 110 [arXiv:1703.09205] [INSPIRE].

  68. [68]

    D. Elander and M. Piai, Glueballs on the Baryonic Branch of Klebanov-Strassler: dimensional deconstruction and a light scalar particle, JHEP06 (2017) 003 [arXiv:1703.10158] [INSPIRE].

  69. [69]

    M. Bianchi, M. Prisco and W. Mueck, New results on holographic three point functions, JHEP11 (2003) 052 [hep-th/0310129] [INSPIRE].

  70. [70]

    M. Berg, M. Haack and W. Mueck, Bulk dynamics in confining gauge theories, Nucl. Phys. B736 (2006) 82 [hep-th/0507285] [INSPIRE].

  71. [71]

    M. Berg, M. Haack and W. Mueck, Glueballs vs. Gluinoballs: Fluctuation Spectra in Non-AdS/Non-CFT, Nucl. Phys. B789 (2008) 1 [hep-th/0612224] [INSPIRE].

  72. [72]

    D. Elander, Glueball Spectra of SQCD-like Theories, JHEP03 (2010) 114 [arXiv:0912.1600] [INSPIRE].

  73. [73]

    D. Elander and M. Piai, Light scalars from a compact fifth dimension, JHEP01 (2011) 026 [arXiv:1010.1964] [INSPIRE].

  74. [74]

    D.K. Hong, J.-W. Lee, B. Lucini, M. Piai and D. Vadacchino, Casimir scaling and Yang-Mills glueballs, Phys. Lett. B775 (2017) 89 [arXiv:1705.00286] [INSPIRE].

  75. [75]

    B. Lucini and M. Panero, SU(N ) gauge theories at large N , Phys. Rept.526 (2013) 93 [arXiv:1210.4997] [INSPIRE].

  76. [76]

    B. Lucini, M. Teper and U. Wenger, Glueballs and k-strings in SU(N ) gauge theories: Calculations with improved operators, JHEP06 (2004) 012 [hep-lat/0404008] [INSPIRE].

  77. [77]

    A. Athenodorou, R. Lau and M. Teper, On the weak N -dependence of SO(N ) and SU(N ) gauge theories in 2+1 dimensions, Phys. Lett. B749 (2015) 448 [arXiv:1504.08126] [INSPIRE].

  78. [78]

    R. Lau and M. Teper, SO(N ) gauge theories in 2 + 1 dimensions: glueball spectra and confinement, JHEP10 (2017) 022 [arXiv:1701.06941] [INSPIRE].

  79. [79]

    M. Teper, SO(4), SO(3) and SU(2) gauge theories in 2 + 1 dimensions: comparing glueball spectra and string tensions, arXiv:1801.05693 [INSPIRE].

  80. [80]

    E. Bennett et al., Sp(4) gauge theory on the lattice: towards SU(4)/Sp(4) composite Higgs (and beyond), JHEP03 (2018) 185 [arXiv:1712.04220] [INSPIRE].

  81. [81]

    J. Holligan et al., Sp(2N ) Yang-Mills towards large N , in 37th International Symposium on Lattice Field Theory, 2019, arXiv:1912.09788 [INSPIRE].

  82. [82]

    A.A. Migdal and M.A. Shifman, Dilaton Effective Lagrangian in Gluodynamics, Phys. Lett. B114 (1982) 445 [INSPIRE].

  83. [83]

    A. Athenodorou et al., Large mass hierarchies from strongly-coupled dynamics, JHEP06 (2016) 114 [arXiv:1605.04258] [INSPIRE].

  84. [84]

    W. Nahm, Supersymmetries and their Representations, Nucl. Phys. B135 (1978) 149 [INSPIRE].

  85. [85]

    V.G. Kac, Lie Superalgebras, Adv. Math.26 (1977) 8 [INSPIRE].

  86. [86]

    B.S. DeWitt and P. van Nieuwenhuizen, Explicit Construction of the Exceptional Superalgebras F (4) and G(3), J. Math. Phys.23 (1982) 1953 [INSPIRE].

  87. [87]

    C. Córdova, G. De Luca and A. Tomasiello, AdS8 Solutions in Type II Supergravity, JHEP07 (2019) 127 [arXiv:1811.06987] [INSPIRE].

  88. [88]

    P. Candelas and X.C. de la Ossa, Comments on Conifolds, Nucl. Phys. B342 (1990) 246 [INSPIRE].

  89. [89]

    A.H. Chamseddine and M.S. Volkov, NonAbelian BPS monopoles in N = 4 gauged supergravity, Phys. Rev. Lett.79 (1997) 3343 [hep-th/9707176] [INSPIRE].

  90. [90]

    I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B536 (1998) 199 [hep-th/9807080] [INSPIRE].

  91. [91]

    I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and chi SB resolution of naked singularities, JHEP08 (2000) 052 [hep-th/0007191] [INSPIRE].

  92. [92]

    J.M. Maldacena and C. Núñez, Towards the large N limit of pure N = 1 superYang-Mills, Phys. Rev. Lett.86 (2001) 588 [hep-th/0008001] [INSPIRE].

  93. [93]

    A. Butti, M. Graña, R. Minasian, M. Petrini and A. Zaffaroni, The Baryonic branch of Klebanov-Strassler solution: A supersymmetric family of SU(3) structure backgrounds, JHEP03 (2005) 069 [hep-th/0412187] [INSPIRE].

  94. [94]

    R.C. Brower, S.D. Mathur and C.-I. Tan, Glueball spectrum for QCD from AdS supergravity duality, Nucl. Phys. B587 (2000) 249 [hep-th/0003115] [INSPIRE].

  95. [95]

    T. Kaluza, Zum Unit¨atsproblem der Physik, Int. J. Mod. Phys. D27 (2018) 1870001 [arXiv:1803.08616] [INSPIRE].

  96. [96]

    L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, Novel local CFT and exact results on perturbations of N = 4 superYang-Mills from AdS dynamics, JHEP12 (1998) 022 [hep-th/9810126] [INSPIRE].

  97. [97]

    J. Distler and F. Zamora, Nonsupersymmetric conformal field theories from stable anti-de Sitter spaces, Adv. Theor. Math. Phys.2 (1999) 1405 [hep-th/9810206] [INSPIRE].

  98. [98]

    L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, The Supergravity dual of N = 1 superYang-Mills theory, Nucl. Phys. B569 (2000) 451 [hep-th/9909047] [INSPIRE].

  99. [99]

    K. Pilch and N.P. Warner, N = 1 supersymmetric renormalization group flows from IIB supergravity, Adv. Theor. Math. Phys.4 (2002) 627 [hep-th/0006066] [INSPIRE].

  100. [100]

    R. Apreda, D.E. Crooks, N.J. Evans and M. Petrini, Confinement, glueballs and strings from deformed AdS, JHEP05 (2004) 065 [hep-th/0308006] [INSPIRE].

  101. [101]

    W. Mueck and M. Prisco, Glueball scattering amplitudes from holography, JHEP04 (2004) 037 [hep-th/0402068] [INSPIRE].

  102. [102]

    M. Petrini, H. Samtleben, S. Schmidt and K. Skenderis, The 10d Uplift of the GPPZ Solution, JHEP07 (2018) 026 [arXiv:1805.01919] [INSPIRE].

  103. [103]

    N. Bobev, F.F. Gautason, B.E. Niehoff and J. van Muiden, Uplifting GPPZ: a ten-dimensional dual of \( \mathcal{N} \) = 1 , JHEP10 (2018) 058 [arXiv:1805.03623] [INSPIRE].

  104. [104]

    J. Polchinski and M.J. Strassler, The String dual of a confining four-dimensional gauge theory, hep-th/0003136 [INSPIRE].

  105. [105]

    L.J. Romans, The F (4) Gauged Supergravity in Six-dimensions, Nucl. Phys. B269 (1986) 691 [INSPIRE].

  106. [106]

    L.J. Romans, Massive N=2a Supergravity in Ten-Dimensions, Phys. Lett. B169 (1986) 374 [INSPIRE].

  107. [107]

    A. Brandhuber and Y. Oz, The D4-D8 brane system and five-dimensional fixed points, Phys. Lett. B460 (1999) 307 [hep-th/9905148] [INSPIRE].

  108. [108]

    M. Cvetič, H. Lü and C.N. Pope, Gauged six-dimensional supergravity from massive type IIA, Phys. Rev. Lett.83 (1999) 5226 [hep-th/9906221] [INSPIRE].

  109. [109]

    J. Hong, J.T. Liu and D.R. Mayerson, Gauged Six-Dimensional Supergravity from Warped IIB Reductions, JHEP09 (2018) 140 [arXiv:1808.04301] [INSPIRE].

  110. [110]

    J. Jeong, O. Kelekci and E. O Colgain, An alternative IIB embedding of F (4) gauged supergravity, JHEP05 (2013) 079 [arXiv:1302.2105] [INSPIRE].

  111. [111]

    R. D’Auria, S. Ferrara and S. Vaula, Matter coupled F (4) supergravity and the AdS6/CFT5correspondence, JHEP10 (2000) 013 [hep-th/0006107] [INSPIRE].

  112. [112]

    L. Andrianopoli, R. D’Auria and S. Vaula, Matter coupled F (4) gauged supergravity Lagrangian, JHEP05 (2001) 065 [hep-th/0104155] [INSPIRE].

  113. [113]

    D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press (2020) [INSPIRE].

  114. [114]

    Y. Tanii, Introduction to supergravity, Springer (2014) [INSPIRE].

  115. [115]

    M. Nishimura, Conformal supergravity from the AdS/CFT correspondence, Nucl. Phys. B588 (2000) 471 [hep-th/0004179] [INSPIRE].

  116. [116]

    S. Ferrara, A. Kehagias, H. Partouche and A. Zaffaroni, AdS6 interpretation of 5-D superconformal field theories, Phys. Lett. B431 (1998) 57 [hep-th/9804006] [INSPIRE].

  117. [117]

    U. Gürsoy, C. Núñez and M. Schvellinger, RG flows from spin(7), CY 4 fold and HK manifolds to AdS, Penrose limits and pp waves, JHEP06 (2002) 015 [hep-th/0203124] [INSPIRE].

  118. [118]

    C. Núñez, I.Y. Park, M. Schvellinger and T.A. Tran, Supergravity duals of gauge theories from F (4) gauged supergravity in six-dimensions, JHEP04 (2001) 025 [hep-th/0103080] [INSPIRE].

  119. [119]

    P. Karndumri, Holographic RG flows in six dimensional F (4) gauged supergravity, JHEP01 (2013) 134 [Erratum ibid.06 (2015) 165] [arXiv:1210.8064] [INSPIRE].

  120. [120]

    Y. Lozano, E. ÓColgáin, D. Rodŕıguez-Gómez and K. Sfetsos, Supersymmetric AdS6via T Duality, Phys. Rev. Lett.110 (2013) 231601 [arXiv:1212.1043] [INSPIRE].

  121. [121]

    C.-K. Wen and H.-X. Yang, QC D4 glueball masses from AdS6black hole description, Mod. Phys. Lett. A20 (2005) 997 [hep-th/0404152] [INSPIRE].

  122. [122]

    S. Kuperstein and J. Sonnenschein, Non-critical, near extremal AdS6 background as a holographic laboratory of four dimensional YM theory, JHEP11 (2004) 026 [hep-th/0411009] [INSPIRE].

  123. [123]

    D. Elander, A.F. Faedo, C. Hoyos, D. Mateos and M. Piai, Multiscale confining dynamics from holographic RG flows, JHEP05 (2014) 003 [arXiv:1312.7160] [INSPIRE].

  124. [124]

    D. Elander, M. Piai and J. Roughley, Holographic glueballs from the circle reduction of Romans supergravity, JHEP02 (2019) 101 [arXiv:1811.01010] [INSPIRE].

  125. [125]

    H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistent nonlinear K K reduction of 11-D supergravity on AdS7× S4and selfduality in odd dimensions, Phys. Lett. B469 (1999) 96 [hep-th/9905075] [INSPIRE].

  126. [126]

    M. Pernici, K. Pilch and P. van Nieuwenhuizen, Gauged Maximally Extended Supergravity in Seven-dimensions, Phys. Lett. B143 (1984) 103 [INSPIRE].

  127. [127]

    M. Pernici, K. Pilch, P. van Nieuwenhuizen and N.P. Warner, Noncompact Gaugings and Critical Points of Maximal Supergravity in Seven-dimensions, Nucl. Phys. B249 (1985) 381 [INSPIRE].

  128. [128]

    H. Lü and C.N. Pope, Exact embedding of N = 1, D = 7 gauged supergravity in D = 11, Phys. Lett. B467 (1999) 67 [hep-th/9906168] [INSPIRE].

  129. [129]

    V.L. Campos, G. Ferretti, H. Larsson, D. Martelli and B.E.W. Nilsson, A Study of holographic renormalization group flows in D = 6 and D = 3, JHEP06 (2000) 023 [hep-th/0003151] [INSPIRE].

  130. [130]

    E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys.2 (1998) 505 [hep-th/9803131] [INSPIRE].

  131. [131]

    T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys.113 (2005) 843 [hep-th/0412141] [INSPIRE].

  132. [132]

    T. Sakai and S. Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys.114 (2005) 1083 [hep-th/0507073] [INSPIRE].

  133. [133]

    C. Csáki, H. Ooguri, Y. Oz and J. Terning, Glueball mass spectrum from supergravity, JHEP01 (1999) 017 [hep-th/9806021] [INSPIRE].

  134. [134]

    D. Teresi, Clockwork without supersymmetry, Phys. Lett. B783 (2018) 1 [arXiv:1802.01591] [INSPIRE].

  135. [135]

    X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP06 (2012) 041 [arXiv:1201.1905] [INSPIRE].

  136. [136]

    R. Emparan, D. Grumiller and K. Tanabe, Large-D gravity and low-D strings, Phys. Rev. Lett.110 (2013) 251102 [arXiv:1303.1995] [INSPIRE].

  137. [137]

    Digital Library of Mathematical Functions https://dlmf.nist.gov/10.21#i.

Download references

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

Author information

Affiliations

Authors

Corresponding author

Correspondence to John Roughley.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 2004.05656

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Verify currency and authenticity via CrossMark

Cite this article

Elander, D., Piai, M. & Roughley, J. Probing the holographic dilaton. J. High Energ. Phys. 2020, 177 (2020). https://doi.org/10.1007/JHEP06(2020)177

Download citation

Keywords

  • AdS-CFT Correspondence
  • Gauge-gravity correspondence