Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-08-14
Phys.Rev.D80:084039,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
LaTeX, 18 pages, 4 figures. Final version accepted for publication in PRD
Scientific paper
10.1103/PhysRevD.80.084039
The Kaluza-Klein compactification in the limit of large number of extra dimensions is studied. Starting point is the Einstein-Hilbert action plus cosmological constant in 4+D dimensions. It is shown that in the large D limit the effective four dimensional cosmological constant is of order 1/D whereas the size of the extra dimensions remains finite. A 't Hooft like large D expansion of the effective Lagrangian for the Kaluza-Klein scalar and gauge fields arising from the dimensional reduction is considered. It is shown that the propagator of the scalar field associated to the determinant of the metric of the extra dimensions is strongly suppressed. This is an interesting result as in standard Kaluza-Klein theory this scalar degree of freedom is responsible for the constraint on the gauge fields which makes it impossible to recover the usual Yang-Mills equations. Moreover in the large D limit it turns out that the ultraviolet divergences due to the interactions between gauge and scalar fields are softened.
Canfora Fabrizio
Giacomini Alex
Zerwekh Alfonso R.
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