Abstract
We show that in brane-world scenarios with warped extra dimensions, the Casimir force due to bulk matter fields may be sufficient to stabilize the radion field φ. In particular, we calculate one loop effective potential for φ, induced by massless scalar fields propagating in the bulk in the Randall–Sundrum background. This potential has a local extremum, which can be a maximum or a minimum depending on the detailed bulk matter content. If the parameters of the background are chosen so that the hierarchy problem is solved geometrically, then the radion mass induced by Casimir corrections is hierarchically smaller than the TeV. Hence, in this important case, we must invoke an alternative mechanism (classical or nonperturbative) which gives the radion a sizable mass so as to make it compatible with observations.
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REFERENCES
Altendorfer, R., Bagger, J., and Nemeschansky, D. (2000). “Supersymmetric Randall–Sundrum Scenario,” hep-th/0003117.
Antoniadis, I., Arkani-Hamed, N., Dimopoulos, S., and Dvali, G. (1998). New dimensions at a millimeter to a Fermi and Superstrigs at a TeV. Physics Letters B, 436, 257; hep-ph/9804398.
Antoniadis, I., Dimopoulos, S., Pomarol, A., and Quiros, M. (1999). “Soft masses in theories with supersymmetry breaking by TeV-compactification,” Nuclear Physics B 544, 503; hep-ph/9810410.
Appelquist, T. and Chodos, A. (1983a). “Quantum effects in Kaluza–Klein theories,” Physical Review Letters 50, 141.
Appelquist, T. and Chodos, A. (1983b). “The Quantum dynamics of Kaluza–Klein theories,” Physical Review D: Particles and Fields 28, 772.
Arkani-Hamed, N., Dimopoulos, S., and Dvali, G. (1998). The hierarchy problem and new dimensions at a millimeter. Physical Letters B 429, 263; hep-ph/9803315.
Arkani-Hamed, N., Dimopoulos, S., and Dvali, G. (1999). Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity. Physical Reviews D: Particles and Fields 59, 86004; hep-ph/9807344.
Birrell, N. D. and Davies, P. C. (1982). Quantum Fields in Curved Space, Cambridge University Press, Cambridge, U.K., 340 pp.
Charmousis, C., Gregory, R., and Rubakov, V. (1999). “Wave function of the radion in a brane world,” hep-th/9912160.
Delgado, A., Pomarol, A., and Quiros, M. (1999). “Supersymmetry and electroweak breaking from extra dimensions at the TeV-scale,” Physical Review D: Particles and Fields 60, 95008; hepph/9812489.
Fabinger, M. and Hořava, P. (2000). “Casimir effect between world-branes in heterotic M-theory,” hep-th/0002073.
Garriga, J., Pujolàs, O., and Tanaka, T. (2000). “Radion effective potential in the brane-world,” hepth/0004109.
Garriga, J. and Tanaka, T. (1999). “Gravity in the Randall–Sundrum brane world,” Physical Review Letters 84, 2778; hep-th/9911055.
Gherghetta, T. and Pomarol, A. (2000). Bulk fields and supersymmetry in a slice of AdS; hepph/0003129.
Goldberger, W. D. and Wise, M. B. (1999). “Modulus stabilization with bulk fields,” Physical Review Letters 83, 4922; hep-ph/9907447.
Goldberger, W.D. and Wise, M. B. (2000). “Phenomenology of a stabilized modulus,” hep-ph/9911457.
Lukas, A., Ovrut, B. A., Stelle, K. S., and Waldram, D. (1999). “The universe as a domain wall,” Physical Review D: Particles and Fields 59, 86001; hep-th/9803235.
Pomarol, A. (1999). “Gauge bosons in a five-dimensional theory with localized gravity,” hepph/9911294.
Pomarol, A. (2000). “Grand unified theories without the desert,” hep-ph/0005293.
Pujolàs, O. (2000). Master's Thesis, unpublished.
Ramond, P. (1989). Field Theory: A Modern Primer, Addison-Wesley, Redwood City, USA, 329 pp.; Frontiers in Physics, vol. 74.
Randall, L. and Sundrum, R. (1999). A large mass hierarchy from a small extra dimension. Physical Review Letters 83, 3370; hep-ph/9905221.
Tanaka, T. and Montes, X. (2000). “Gravity in the brane-world for two-branes model with stabilized modulus,” hep-th/0001092.
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Pujolàs, O. Effective Potential in Brane-World Scenarios. International Journal of Theoretical Physics 40, 2131–2142 (2001). https://doi.org/10.1023/A:1012925918545
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DOI: https://doi.org/10.1023/A:1012925918545