Kaluza-Klein theory in the limit of large number of extra dimensions

Abstract

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.

arXiv commentLaTeX, 18 pages, 4 figures. Final version accepted for publication in PRD

References in corpus (6)

• Kaluza-Klein Gravity
• Flux Compactification
• General Relativity with small cosmological constant from spontaneous compactification of Lovelock theory in vacuum
• Quantum gravity at a large number of dimensions
• A Large N expansion for Gravity
• The UV behavior of Gravity at Large N

Cited by in corpus (9)

• The large D limit of General Relativity
• The Large D Limit of Einstein's Equations
• Dynamical compactification in Einstein-Gauss-Bonnet gravity from geometric frustration
• Friedmann dynamics recovered from compactified Einstein-Gauss-Bonnet cosmology
• The large D limit of dimensionally continued gravity
• Statefinder Parameters for Different Dark Energy Models with Variable G Correction in Kaluza-Klein Cosmology
• Kaluza-Klein Reduction of a Quadratic Curvature Model
• Extra Dimensional Curvature Supression of the Effective Four Dimensional Vacuum Energy Density
• Small black holes in the large D limit