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

Understand

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.