Radion and moduli stabilization from induced brane actions in higher-dimensional brane worlds

We consider a 4+N-dimensional brane world with 2 co-dimension 1 branes in an empty bulk. The two branes have N-1 of their extra dimensions compactified on a sphere S^(N-1), whereas the ordinary 4 spacetime directions are Poincare invariant. An essential input are induced stress-energy tensors on the branes providing different tensions for the spherical and flat part of the branes. The junction conditions - notably through their extra dimensional components - fix both the distance between the branes as well as the size of the sphere. As a result, we demonstrate, that there are no scalar Kaluza-Klein states at all (massless or massive), that would correspond to a radion or a modulus field of S^(N-1). We also discuss the effect of induced Einstein terms on the branes and show that their coefficients are bounded from above, otherwise they lead to a graviton ghost.