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

TL;DR

This paper investigates the behavior of Kaluza-Klein theories as the number of extra dimensions becomes very large, revealing that the effective four-dimensional cosmological constant diminishes and scalar field propagators are suppressed, affecting gauge field constraints.

Contribution

It introduces a large D expansion approach to analyze Kaluza-Klein compactification, showing suppression of scalar propagators and softened divergences in the large extra dimension limit.

Findings

Effective 4D cosmological constant scales as 1/D.

Scalar propagator is strongly suppressed at large D.

Ultraviolet divergences are softened in the large D limit.

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.