Dimensionally reducing the classical Regge growth conjecture

We explore the classical Regge growth conjecture in the 4d effective field theory that results from compactifying $D$-dimensional General Relativity on a compact, Ricci-flat manifold. While the higher dimensional description is given in terms of pure Einstein gravity and the conjecture is automatically satisfied, it imposes several non-trivial constraints in the 4d spectrum. Namely, there must be either none or an infinite number of massive spin-2 modes, and the mass ratio between consecutive Kaluza-Klain spin-2 replicas is bounded by the 4d coupling constants.