Abstract
This work sets up a general theoretical framework to study stability of models with a warped extra dimension where N scalar fields couple minimally to gravity. Our analysis encompasses Randall-Sundrum models with branes and bulk scalars, and general domain-wall models. We derive the Schrödinger equation governing the spin-0 spectrum of perturbations of such a system. This result is specialized to potentials generated using fake supergravity, and we show that models without branes are free of tachyonic modes. Turning to the existence of zero modes, we prove a criterion which relates the number of normalizable zero modes to the parities of the scalar fields. Constructions with definite parity and only odd scalars are shown to be free of zero modes and are hence perturbatively stable. We give two explicit examples of domain-wall models with a soft wall, one which admits a zero mode and one which does not. The latter is an example of a model that stabilizes a compact extra dimension using only bulk scalars and does not require dynamical branes.
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References
I. Antoniadis, A possible new dimension at a few TeV, Phys. Lett. B 246 (1990) 377 [SPIRES].
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].
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].
L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [SPIRES].
L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [SPIRES].
V.A. Rubakov and M.E. Shaposhnikov, Do we live inside a domain wall?, Phys. Lett. B 125 (1983) 136 [SPIRES].
A. Kehagias and K. Tamvakis, Localized gravitons, gauge bosons and chiral fermions in smooth spaces generated by a bounce, Phys. Lett. B 504 (2001) 38 [hep-th/0010112] [SPIRES].
R. Davies, D.P. George and R.R. Volkas, The standard model on a domain-wall brane, Phys. Rev. D 77 (2008) 124038 [arXiv:0705.1584] [SPIRES].
C. Csáki, J. Erlich, T.J. Hollowood and Y. Shirman, Universal aspects of gravity localized on thick branes, Nucl. Phys. B 581 (2000) 309 [hep-th/0001033] [SPIRES].
A. Karch, E. Katz, D.T. Son and M.A. Stephanov, Linear Confinement and AdS/QCD, Phys. Rev. D 74 (2006) 015005 [hep-ph/0602229] [SPIRES].
B. Batell and T. Gherghetta, Dynamical soft-wall AdS/QCD, Phys. Rev. D 78 (2008) 026002 [arXiv:0801.4383] [SPIRES].
A. Falkowski and M. Pérez-Victoria, Electroweak breaking on a soft wall, JHEP 12 (2008) 107 [arXiv:0806.1737] [SPIRES].
B. Batell, T. Gherghetta and D. Sword, The soft-wall standard model, Phys. Rev. D 78 (2008) 116011 [arXiv:0808.3977] [SPIRES].
A. Delgado and D. Diego, Fermion mass hierarchy from the soft wall, Phys. Rev. D 80 (2009) 024030 [arXiv:0905.1095] [SPIRES].
S. Mert Aybat and J. Santiago, Bulk fermions in warped models with a soft wall, Phys. Rev. D 80 (2009) 035005 [arXiv:0905.3032] [SPIRES].
T. Gherghetta and D. Sword, Fermion flavor in soft-wall AdS, Phys. Rev. D 80 (2009) 065015 [arXiv:0907.3523] [SPIRES].
J.A. Cabrer, G. von Gersdorff and M. Quirós, Soft-wall stabilization, New J. Phys. 12 (2010) 075012 [arXiv:0907.5361] [SPIRES].
G. von Gersdorff, From soft walls to infrared branes, arXiv:1005.5134 [SPIRES].
G. Cacciapaglia, G. Marandella and J. Terning, The AdS/CFT/unparticle correspondence, JHEP 02 (2009) 049 [arXiv:0804.0424] [SPIRES].
A. Falkowski and M. Pérez-Victoria, Holographic unhiggs, Phys. Rev. D 79 (2009) 035005 [arXiv:0810.4940] [SPIRES].
W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447] [SPIRES].
C. Csáki, M.L. Graesser and G.D. Kribs, Radion dynamics and electroweak physics, Phys. Rev. D 63 (2001) 065002 [hep-th/0008151] [SPIRES].
M. Toharia and M. Trodden, Metastable kinks in the orbifold, Phys. Rev. Lett. 100 (2008) 041602 [arXiv:0708.4005] [SPIRES].
M. Toharia and M. Trodden, Existence and stability of non-trivial scalar field configurations in orbifolded extra dimensions, Phys. Rev. D 77 (2008) 025029 [arXiv:0708.4008] [SPIRES].
S. Kobayashi, K. Koyama and J. Soda, Thick brane worlds and their stability, Phys. Rev. D 65 (2002) 064014 [hep-th/0107025] [SPIRES].
M. Toharia, Odd tachyons in compact extra dimensions, arXiv:0803.2503 [SPIRES].
M. Toharia, M. Trodden and E.J. West, Scalar kinks in warped extra dimensions, Phys. Rev. D 82 (2010) 025009 [arXiv:1002.0011] [SPIRES].
O. DeWolfe, D.Z. Freedman, S.S. Gubser and A. Karch, Modeling the fifth dimension with scalars and gravity, Phys. Rev. D 62 (2000) 046008 [hep-th/9909134] [SPIRES].
D.Z. Freedman, C. Núñez, M. Schnabl and K. Skenderis, Fake supergravity and domain wall stability, Phys. Rev. D 69 (2004) 104027 [hep-th/0312055] [SPIRES].
O. DeWolfe and D.Z. Freedman, Notes on fluctuations and correlation functions in holographic renormalization group flows, hep-th/0002226 [SPIRES].
D. Bazeia, M.M. Ferreira, A.R. Gomes and R. Menezes, Lorentz-violating effects on topological defects generated by two real scalar fields, Physica D 239 (2010) 942 [arXiv:1001.5286] [SPIRES].
F. Cooper, A. Khare and U. Sukhatme, Supersymmetry and quantum mechanics, Phys. Rept. 251 (1995) 267 [hep-th/9405029] [SPIRES].
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Mert Aybat, S., George, D.P. Stability of scalar fields in warped extra dimensions. J. High Energ. Phys. 2010, 10 (2010). https://doi.org/10.1007/JHEP09(2010)010
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DOI: https://doi.org/10.1007/JHEP09(2010)010