Journal of High Energy Physics

, 2016:25 | Cite as

Fine-tuning with brane-localized flux in 6D supergravity

Open Access
Regular Article - Theoretical Physics

Abstract

There are claims in the literature that the cosmological constant problem could be solved in a braneworld model with two large (micron-sized) supersymmetric extra dimensions. The mechanism relies on two basic ingredients: first, the cosmological constant only curves the compact bulk geometry into a rugby shape while the 4D curvature stays flat. Second, a brane-localized flux term is introduced in order to circumvent Weinberg’s fine-tuning argument, which otherwise enters here through a backdoor via the flux quantization condition. In this paper, we show that the latter mechanism does not work in the way it was designed: the only localized flux coupling that guarantees a flat on-brane geometry is one which preserves the scale invariance of the bulk theory. Consequently, Weinberg’s argument applies, making a fine-tuning necessary again. The only remaining window of opportunity lies within scale invariance breaking brane couplings, for which the tuning could be avoided. Whether the corresponding 4D curvature could be kept under control and in agreement with the observed value will be answered in our companion paper [1].

Keywords

Large Extra Dimensions Effective field theories Supersymmetric 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]
    F. Niedermann and R. Schneider, SLED Phenomenology: Curvature vs. Volume, arXiv:1512.03800 [INSPIRE].
  2. [2]
    S. Weinberg, The Cosmological Constant Problem, Rev. Mod. Phys. 61 (1989) 1 [INSPIRE].CrossRefADSMathSciNetMATHGoogle Scholar
  3. [3]
    V.A. Rubakov and M.E. Shaposhnikov, Extra Space-Time Dimensions: Towards a Solution to the Cosmological Constant Problem, Phys. Lett. B 125 (1983) 139 [INSPIRE].CrossRefADSGoogle Scholar
  4. [4]
    J.-W. Chen, M.A. Luty and E. Ponton, A critical cosmological constant from millimeter extra dimensions, JHEP 09 (2000) 012 [hep-th/0003067] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  5. [5]
    S.M. Carroll and M.M. Guica, Sidestepping the cosmological constant with football shaped extra dimensions, hep-th/0302067 [INSPIRE].
  6. [6]
    I. Navarro, Codimension two compactifications and the cosmological constant problem, JCAP 09 (2003) 004 [hep-th/0302129] [INSPIRE].CrossRefADSGoogle Scholar
  7. [7]
    G.R. Dvali, G. Gabadadze and M. Porrati, 4-D gravity on a brane in 5-D Minkowski space, Phys. Lett. B 485 (2000) 208 [hep-th/0005016] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  8. [8]
    L. Eglseer, F. Niedermann and R. Schneider, Brane induced gravity: Ghosts and naturalness, Phys. Rev. D 92 (2015) 084029 [arXiv:1506.02666] [INSPIRE].ADSGoogle Scholar
  9. [9]
    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] [INSPIRE].
  10. [10]
    N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity, Phys. Rev. D 59 (1999) 086004 [hep-ph/9807344] [INSPIRE].
  11. [11]
    D.J. Kapner et al., Tests of the gravitational inverse-square law below the dark-energy length scale, Phys. Rev. Lett. 98 (2007) 021101 [hep-ph/0611184] [INSPIRE].
  12. [12]
    A. Joyce, B. Jain, J. Khoury and M. Trodden, Beyond the Cosmological Standard Model, Phys. Rept. 568 (2015) 1 [arXiv:1407.0059] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  13. [13]
    F. Leblond, R.C. Myers and D.J. Winters, Consistency conditions for brane worlds in arbitrary dimensions, JHEP 07 (2001) 031 [hep-th/0106140] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  14. [14]
    J.M. Cline, J. Descheneau, M. Giovannini and J. Vinet, Cosmology of codimension two brane worlds, JHEP 06 (2003) 048 [hep-th/0304147] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  15. [15]
    Y. Aghababaie, C.P. Burgess, S.L. Parameswaran and F. Quevedo, Towards a naturally small cosmological constant from branes in 6 − D supergravity, Nucl. Phys. B 680 (2004) 389 [hep-th/0304256] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  16. [16]
    C.P. Burgess and L. van Nierop, Large Dimensions and Small Curvatures from Supersymmetric Brane Back-reaction, JHEP 04 (2011) 078 [arXiv:1101.0152] [INSPIRE].CrossRefADSGoogle Scholar
  17. [17]
    C.P. Burgess and L. van Nierop, Technically Natural Cosmological Constant From Supersymmetric 6D Brane Backreaction, Phys. Dark Univ. 2 (2013) 1 [arXiv:1108.0345] [INSPIRE].CrossRefGoogle Scholar
  18. [18]
    C.P. Burgess, R. Diener and M. Williams, The Gravity of Dark Vortices: Effective Field Theory for Branes and Strings Carrying Localized Flux, JHEP 11 (2015) 049 [arXiv:1506.08095] [INSPIRE].CrossRefADSGoogle Scholar
  19. [19]
    C.P. Burgess, R. Diener and M. Williams, EFT for Vortices with Dilaton-dependent Localized Flux, JHEP 11 (2015) 054 [arXiv:1508.00856] [INSPIRE].CrossRefADSGoogle Scholar
  20. [20]
    S. Weinberg, Gravitation and Cosmology. Principles and Applications of the General Theory of Relativity, John Wiley & Sons, Inc., New York, U.S.A. (1972).Google Scholar
  21. [21]
    S. Randjbar-Daemi, A. Salam and J.A. Strathdee, Spontaneous Compactification in Six-Dimensional Einstein-Maxwell Theory, Nucl. Phys. B 214 (1983) 491 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  22. [22]
    C.P. Burgess, The Cosmological Constant Problem: Why it’s hard to get Dark Energy from Micro-physics, in proceedings of 100e Ecole d’Ete de Physique: Post-Planck Cosmology Les Houches, France, July 8 - August 2 2013, arXiv:1309.4133 [INSPIRE].
  23. [23]
    G.W. Gibbons, R. Güven and C.N. Pope, 3-branes and uniqueness of the Salam-Sezgin vacuum, Phys. Lett. B 595 (2004) 498 [hep-th/0307238] [INSPIRE].CrossRefADSGoogle Scholar
  24. [24]
    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] [INSPIRE].CrossRefADSGoogle Scholar
  25. [25]
    C.P. Burgess, L. van Nierop and M. Williams, Distributed SUSY breaking: dark energy, Newton’s law and the LHC, JHEP 07 (2014) 034 [arXiv:1311.3911] [INSPIRE].CrossRefADSGoogle Scholar
  26. [26]
    J. Garriga and M. Porrati, Football shaped extra dimensions and the absence of self-tuning, JHEP 08 (2004) 028 [hep-th/0406158] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  27. [27]
    I. Navarro, Spheres, deficit angles and the cosmological constant, Class. Quant. Grav. 20 (2003) 3603 [hep-th/0305014] [INSPIRE].CrossRefADSMATHGoogle Scholar
  28. [28]
    H.-P. Nilles, A. Papazoglou and G. Tasinato, Selftuning and its footprints, Nucl. Phys. B 677 (2004) 405 [hep-th/0309042] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  29. [29]
    C.P. Burgess, R. Diener and M. Williams, Self-Tuning at Large (Distances): 4D Description of Runaway Dilaton Capture, JHEP 10 (2015) 177 [arXiv:1509.04209] [INSPIRE].CrossRefADSGoogle Scholar
  30. [30]
    C.P. Burgess, R. Diener and M. Williams, A problem with δ-functions: stress-energy constraints on bulk-brane matching (with comments on arXiv:1508.01124), JHEP 01 (2016) 017 [arXiv:1509.04201] [INSPIRE].

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Arnold Sommerfeld Center for Theoretical PhysicsLudwig-Maximilians-UniversitätMunichGermany
  2. 2.Excellence Cluster UniverseGarchingGermany

Personalised recommendations