Boson mass spectrum of Kaluza-Klein theories on hyperspheres

We derive the mass spectrum of a (4 + d)-dimensional Einstein-Yang-Mills theory with gauge group SO(d), spontaneously compactified to four dimensions. The background manifold is the product of four-dimensional flat space and a d-sphere with Killing-metric. The Yang-Mills field has a classical value equal to the spin connection on the sphere. Using harmonic expansions, we calculate the mass spectrum for spin-2, spin-1 and spin-0 bosons. The theory is found to be classically stable for d not= 3 and has no massless scalar bosons for d not= 4. (orig.)