Skip to main content
SpringerLink
Log in

Bulk axions, brane back-reaction and fluxes

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

Extra-dimensional models can involve bulk pseudo-Goldstone bosons (pGBs) whose shift symmetry is explicitly broken only by physics localized on branes. Reliable calculation of their low-energy potential is often difficult because it requires an understanding of the dynamics that stabilizes the geometry of the extra dimensions. Rugby ball solutions provide simple examples of extra-dimensional configurations for which two compact extra dimensions are stabilized in the presence of only positive-tension brane sources. The effects of brane back-reaction can be computed explicitly for these systems, allowing the calculation of the shape of the low-energy pGB potential, V 4D (φ), as a function of the perturbing brane properties, as well as the response of both the extra dimensional and on-brane geometries to this stabilization. If the φ-dependence is a small part of the total brane tension a very general analysis is possible, permitting an exploration of how the system responds to frustration when the two branes disagree on what the proper scalar vacuum should be. We show how the low-energy potential is given by the sum of brane tensions (in agreement with common lore) when only the brane tensions couple to φ. We also show how a direct brane coupling to the flux stabilizing the extra dimensions corrects this result in a way that does not simply amount to the contribution of the flux to the brane tensions. The mass of the low-energy pseudo-Goldstone mode is of order m a ∼ (μ/F)2 m KK (where μ is the energy scale associated with the brane symmetry breaking and F < M p is the extra-dimensional axion decay constant). In principle this can be larger or smaller than the Kaluza-Klein scale, m KK, but when it is larger axion properties cannot be computed purely within a 4D approximation (as they usually are). We briefly describe several potential applications, including a brane realization of ‘natural inflation,’ and a dynamical mechanism for suppressing the couplings of the pGB to matter localized on the branes. Since the scalar can be light enough to be relevant to precision tests of gravity (in a technically natural way) this mechanism can be relevant to evading phenomenological bounds.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, The hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429 (1998) 263 [hep-ph/9803315] [SPIRES].

    ADS  Google Scholar 

  2. N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, Phenomenology, astrophysics and cosmology of theories with sub-millimeter dimensions and TeV scale quantum gravity, Phys. Rev. D 59 (1999) 086004 [hep-ph/9807344] [SPIRES].

    ADS  Google Scholar 

  3. I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, New dimensions at a millimeter to a Fermi and superstrings at a TeV, Phys. Lett. B 436 (1998) 257 [hep-ph/9804398] [SPIRES].

    ADS  Google Scholar 

  4. K. Benakli, Phenomenology of low quantum gravity scale models, Phys. Rev. D 60 (1999) 104002 [hep-ph/9809582] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  5. C.P. Burgess, L.E. Ibáñez and F. Quevedo, Strings at the intermediate scale or is the Fermi scale dual to the Planck scale?, Phys. Lett. B 447 (1999) 257 [hep-ph/9810535] [SPIRES].

    ADS  Google Scholar 

  6. P. Hořava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142] [SPIRES].

    ADS  Google Scholar 

  7. P. Hořava and E. Witten, Heterotic and type-I string dynamics from eleven dimensions, Nucl. Phys. B 460 (1996) 506 [hep-th/9510209] [SPIRES].

    ADS  Google Scholar 

  8. E. Witten, Strong coupling expansion of Calabi-Yau compactification, Nucl. Phys. B 471 (1996) 135 [hep-th/9602070] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. J.D. Lykken, Weak scale superstrings, Phys. Rev. D 54 (1996) 3693 [hep-th/9603133] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  10. L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. P. Binetruy, C. Deffayet and D. Langlois, Non-conventional cosmology from a brane-universe, Nucl. Phys. B 565 (2000) 269 [hep-th/9905012] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  14. P. Kanti, I.I. Kogan, K.A. Olive and M. Pospelov, Cosmological 3-brane solutions, Phys. Lett. B 468 (1999) 31 [hep-ph/9909481] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  15. J.M. Cline, C. Grojean and G. Servant, Cosmological expansion in the presence of extra dimensions, Phys. Rev. Lett. 83 (1999) 4245 [hep-ph/9906523] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. B.R. Greene, A.D. Shapere, C. Vafa and S.-T. Yau, Stringy cosmic strings and noncompact Calabi-Yau manifolds, Nucl. Phys. B 337 (1990) 1 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. S. Kachru et al., Towards inflation in string theory, JCAP 10 (2003) 013 [hep-th/0308055] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  18. D. Baumann et al., On D3-brane potentials in compactifications with fluxes and wrapped D-branes, JHEP 11 (2006) 031 [hep-th/0607050] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. D. Baumann, A. Dymarsky, I.R. Klebanov and L. McAllister, Towards an explicit model of D-brane inflation, JCAP 01 (2008) 024 [arXiv:0706.0360] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  20. A. Kehagias, A conical tear drop as a vacuum-energy drain for the solution of the cosmological constant problem, Phys. Lett. B 600 (2004) 133 [hep-th/0406025] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  21. T. Kobayashi and M. Minamitsuji, Brane cosmological solutions in six-dimensional warped flux compactifications, JCAP 07 (2007) 016 [arXiv:0705.3500] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  22. D. Kiley, Rotating black holes on codimension-2 branes, Phys. Rev. D 76 (2007) 126002 [arXiv:0708.1016] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  23. F. Leblond, R.C. Myers and D.J. Winters, Consistency conditions for brane worlds in arbitrary dimensions, JHEP 07 (2001) 031 [hep-th/0106140] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  24. S.M. Carroll and M.M. Guica, Sidestepping the cosmological constant with football-shaped extra dimensions, hep-th/0302067 [SPIRES].

  25. I. Navarro, Codimension two compactifications and the cosmological constant problem, JCAP 09 (2003) 004 [hep-th/0302129] [SPIRES].

    ADS  Google Scholar 

  26. E. Papantonopoulos and A. Papazoglou, Brane-bulk matter relation for a purely conical codimension-2 brane world, JCAP 07 (2005) 004 [hep-th/0501112] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  27. A. Salam and E. Sezgin, Chiral compactification on Minkowski x S 2 of N = 2 Einstein-Maxwell supergravity in six-dimensions, Phys. Lett. B 147 (1984) 47 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  28. Y. Aghababaie, C.P. Burgess, S.L. Parameswaran and F. Quevedo, Towards a naturally small cosmological constant from branes in 6D supergravity, Nucl. Phys. B 680 (2004) 389 [hep-th/0304256] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  29. S.L. Parameswaran, G. Tasinato and I. Zavala, The 6D superswirl, Nucl. Phys. B 737 (2006) 49 [hep-th/0509061] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  30. H.M. Lee and C. Lüdeling, The general warped solution with conical branes in six-dimensional supergravity, JHEP 01 (2006) 062 [hep-th/0510026] [SPIRES].

    Article  ADS  Google Scholar 

  31. H.M. Lee and A. Papazoglou, Supersymmetric codimension-two branes in six-dimensional gauged supergravity, JHEP 01 (2008) 008 [arXiv:0710.4319] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  32. C.P. Burgess, S.L. Parameswaran and I. Zavala, The fate of unstable gauge flux compactifications, JHEP 05 (2009) 008 [arXiv:0812.3902] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  33. C.P. Burgess, Goldstone and pseudo-Goldstone bosons in nuclear, particle and condensed-matter physics, Phys. Rept. 330 (2000) 193 [hep-th/9808176] [SPIRES].

    Article  ADS  Google Scholar 

  34. C.P. Burgess, D. Hoover and G. Tasinato, UV caps and modulus stabilization for 6D gauged chiral supergravity, JHEP 09 (2007) 124 [arXiv:0705.3212] [SPIRES].

    Article  ADS  Google Scholar 

  35. C.P. Burgess, D. Hoover, C. de Rham and G. Tasinato, Effective field theories and matching for codimension-2 branes, JHEP 03 (2009) 124 [arXiv:0812.3820] [SPIRES].

    Article  ADS  Google Scholar 

  36. C.P. Burgess, D. Hoover and G. Tasinato, Technical naturalness on a codimension-2 brane, JHEP 06 (2009) 014 [arXiv:0903.0402] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  37. A. Bayntun, C.P. Burgess and L. van Nierop, Codimension-2 brane-bulk matching: examples from six and ten dimensions, New J. Phys. 12 (2010) 075015 [arXiv:0912.3039] [SPIRES].

    Article  ADS  Google Scholar 

  38. P. Bostock, R. Gregory, I. Navarro and J. Santiago, Einstein gravity on the codimension 2 brane?, Phys. Rev. Lett. 92 (2004) 221601 [hep-th/0311074] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  39. I. Navarro and J. Santiago, Gravity on codimension 2 brane worlds, JHEP 02 (2005) 007 [hep-th/0411250] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  40. J. Vinet and J.M. Cline, Codimension-two branes in six-dimensional supergravity and the cosmological constant problem, Phys. Rev. D 71 (2005) 064011 [hep-th/0501098] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  41. M. Peloso, L. Sorbo and G. Tasinato, Standard 4d gravity on a brane in six dimensional flux compactifications, Phys. Rev. D 73 (2006) 104025 [hep-th/0603026] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  42. B. Himmetoglu and M. Peloso, Isolated Minkowski vacua and stability analysis for an extended brane in the rugby ball, Nucl. Phys. B 773 (2007) 84 [hep-th/0612140] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  43. B. Himmetoglu and M. Peloso, Isolated Minkowski vacua and stability analysis for an extended brane in the rugby ball, Nucl. Phys. B 773 (2007) 84 [hep-th/0612140] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  44. E. Papantonopoulos, A. Papazoglou and V. Zamarias, Regularization of conical singularities in warped six-dimensional compactifications, JHEP 03 (2007) 002 [hep-th/0611311] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  45. E. Papantonopoulos, A. Papazoglou and V. Zamarias, Induced cosmology on a regularized brane in six-dimensional flux compactification, Nucl. Phys. B 797 (2008) 520 [arXiv:0707.1396] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  46. D. Yamauchi and M. Sasaki, Brane world in arbitrary dimensions without Z 2 symmetry, Prog. Theor. Phys. 118 (2007) 245 [arXiv:0705.2443] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  47. N. Kaloper and D. Kiley, Charting the landscape of modified gravity, JHEP 05 (2007) 045 [hep-th/0703190] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  48. M. Minamitsuji and D. Langlois, Cosmological evolution of regularized branes in 6D warped flux compactifications, Phys. Rev. D 76 (2007) 084031 [arXiv:0707.1426] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  49. S.A. Appleby and R.A. Battye, Regularized braneworlds of arbitrary codimension, Phys. Rev. D 76 (2007) 124009 [arXiv:0707.4238] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  50. C. Bogdanos, A. Kehagias and K. Tamvakis, Pseudo-3-branes in a curved 6D bulk, Phys. Lett. B 656 (2007) 112 [arXiv:0709.0873] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  51. O. Corradini, K. Koyama and G. Tasinato, Induced gravity on intersecting brane-worlds Part I: Maximally symmetric solutions, Phys. Rev. D 77 (2008) 084006 [arXiv:0712.0385] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  52. F. Arroja, T. Kobayashi, K. Koyama and T. Shiromizu, Low energy effective theory on a regularized brane in 6D gauged chiral supergravity, JCAP 12 (2007) 006 [arXiv:0710.2539] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  53. O. Corradini, K. Koyama and G. Tasinato, Induced gravity on intersecting brane-worlds Part II: Cosmology, Phys. Rev. D 78 (2008) 124002 [arXiv:0803.1850] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  54. V. Dzhunushaliev, V. Folomeev and M. Minamitsuji, Thick brane solutions, Rept. Prog. Phys. 73 (2010) 066901 [arXiv:0904.1775] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  55. K. Lanczos, Bemerkung zur de Sitterschen welt, Phys. Z. 23 (1922) 239.

    Google Scholar 

  56. K. Lanczos, Flächenhafte verteilung der materie in der Einsteinschen gravitationstheorie, Ann. Phys. 74 (1924) 518.

    Article  MATH  Google Scholar 

  57. C.W. Misner and D.H. Sharp, Relativistic equations for adiabatic, spherically symmetric gravitational collapse, Phys. Rev. B 136 (1964) 571.

    Article  MathSciNet  ADS  Google Scholar 

  58. W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuov. Cim. 44B (1966) 1 [Erratum ibid. 48B (1966) 463].

    ADS  Google Scholar 

  59. T. Damour and A.M. Polyakov, The string dilaton and a least coupling principle, Nucl. Phys. B 423 (1994) 532 [hep-th/9401069] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  60. P. Brax, C. van de Bruck, A.-C. Davis and D. Shaw, The dilaton and modified gravity, Phys. Rev. D 82 (2010) 063519 [arXiv:1005.3735] [SPIRES].

    ADS  Google Scholar 

  61. E. Dudas, C. Papineau and V.A. Rubakov, Flowing to four dimensions, JHEP 03 (2006) 085 [hep-th/0512276] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  62. E. Dudas and C. Papineau, Dual realizations of dynamical symmetry breaking, JHEP 11 (2006) 010 [hep-th/0608054] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  63. C.P. Burgess, C. de Rham and L. van Nierop, The hierarchy problem and the self-localized Higgs, JHEP 08 (2008) 061 [arXiv:0802.4221] [SPIRES].

    Article  ADS  Google Scholar 

  64. S. Weinberg, Gravitation and cosmology, Wiley, New York, U.S.A. (1973).

    Google Scholar 

  65. C.W. Misner, J.A. Wheeler and K.S. Thorne, Gravitation, W.H. Freeman & Company, Reading, England (1973).

    Google Scholar 

  66. A. Vilenkin, Gravitational field of vacuum domain walls and strings, Phys. Rev. D 23 (1981) 852 [SPIRES].

    ADS  Google Scholar 

  67. W.A. Hiscock, Exact gravitational field of a string, Phys. Rev. D 31 (1985) 3288 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  68. A.J. Tolley, C.P. Burgess, C. de Rham and D. Hoover, Scaling solutions to 6D gauged chiral supergravity, New J. Phys. 8 (2006) 324 [hep-th/0608083] [SPIRES].

    Article  ADS  Google Scholar 

  69. A.J. Tolley, C.P. Burgess, C. de Rham and D. Hoover, Exact wave solutions to 6D gauged chiral supergravity, JHEP 07 (2008) 075 [arXiv:0710.3769] [SPIRES].

    Article  ADS  Google Scholar 

  70. M. Minamitsuji, Instability of brane cosmological solutions with flux compactifications, Class. Quant. Grav. 25 (2008) 075019 [arXiv:0801.3080] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  71. H.M. Lee and A. Papazoglou, Codimension-2 brane inflation, Phys. Rev. D 80 (2009) 043506 [arXiv:0901.4962] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  72. H.M. Lee and A. Papazoglou, Scalar mode analysis of the warped Salam-Sezgin model, Nucl. Phys. B 747 (2006) 294 [hep-th/0602208] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  73. C.P. Burgess, C. de Rham, D. Hoover, D. Mason and A.J. Tolley, Kicking the rugby ball: Perturbations of 6D gauged chiral supergravity, JCAP 02 (2007) 009 [hep-th/0610078] [SPIRES].

    ADS  Google Scholar 

  74. S.L. Parameswaran, S. Randjbar-Daemi and A. Salvio, Gauge fields, fermions and mass gaps in 6D brane worlds, Nucl. Phys. B 767 (2007) 54 [hep-th/0608074] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  75. S.L. Parameswaran, S. Randjbar-Daemi and A. Salvio, Stability and negative tensions in 6D brane worlds, JHEP 01 (2008) 051 [arXiv:0706.1893] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  76. S.L. Parameswaran, S. Randjbar-Daemi and A. Salvio, General perturbations for braneworld compactifications and the six dimensional case, JHEP 03 (2009) 136 [arXiv:0902.0375] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  77. W.D. Goldberger and M.B. Wise, Renormalization group flows for brane couplings, Phys. Rev. D 65 (2002) 025011 [hep-th/0104170] [SPIRES].

    ADS  Google Scholar 

  78. E. Dudas, C. Papineau and V.A. Rubakov, Flowing to four dimensions, JHEP 03 (2006) 085 [hep-th/0512276] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  79. C. de Rham, The effective field theory of codimension-two branes, JHEP 01 (2008) 060 [arXiv:0707.0884] [SPIRES].

    Article  Google Scholar 

  80. F. del Aguila, M. Pérez-Victoria and J. Santiago, Effective description of brane terms in extra dimensions, JHEP 10 (2006) 056 [hep-ph/0601222] [SPIRES].

    Article  Google Scholar 

  81. K.A. Milton, S.D. Odintsov and S. Zerbini, Bulk versus brane running couplings, Phys. Rev. D 65 (2002) 065012 [hep-th/0110051] [SPIRES].

    ADS  Google Scholar 

  82. C.P. Burgess, Quantum gravity in everyday life: General relativity as an effective field theory, Living Rev. Rel. 7 (2004) 5 [gr-qc/0311082] [SPIRES].

    Google Scholar 

  83. J.F. Donoghue, Introduction to the effective field theory description of gravity, gr-qc/9512024 [SPIRES].

  84. C.P. Burgess, P. Grenier and D. Hoover, Quintessentially flat scalar potentials, JCAP 03 (2004) 008 [hep-ph/0308252] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  85. K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo Nambu-Goldstone bosons, Phys. Rev. Lett. 65 (1990) 3233 [SPIRES].

    Article  ADS  Google Scholar 

  86. C.M. Will, The confrontation between general relativity and experiment, Living Rev. Rel. 9 (2005) 3 [gr-qc/0510072] [SPIRES].

    Google Scholar 

  87. E.G. Adelberger, B.R. Heckel and A.E. Nelson, Tests of the gravitational inverse-square law, Ann. Rev. Nucl. Part. Sci. 53 (2003) 77 [hep-ph/0307284] [SPIRES].

    Article  ADS  Google Scholar 

  88. C. Brans and R.H. Dicke, Mach’s principle and a relativistic theory of gravitation, Phys. Rev. 124 (1961) 925 [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics & Astronomy, McMaster University, 1280 Main Street West, Hamilton, ON, Canada

    C. P. Burgess & L. van Nierop

  2. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, Canada

    C. P. Burgess

Authors
  1. C. P. Burgess
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. van Nierop
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. van Nierop.

Additional information

ArXiv ePrint: 1012.2638

Rights and permissions

Reprints and permissions

About this article

Cite this article

Burgess, C.P., van Nierop, L. Bulk axions, brane back-reaction and fluxes. J. High Energ. Phys. 2011, 94 (2011). https://doi.org/10.1007/JHEP02(2011)094

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP02(2011)094

Keywords

Search

Navigation