Graviton scattering and bootstrap bounds

Scattering amplitudes of massive spin-2 particles generically grow with energy and lead to violations of perturbative unitarity. One way to partially soften such amplitudes is with the infinite towers of particles present in Kaluza-Klein theories. In this talk, I will discuss this mechanism of unitarization and how it leads to a bootstrap procedure, analogous to the conformal bootstrap, that yields constraints on the eigenfunctions and eigenvalues of the Laplacian on closed manifolds.