High-energy behavior of ghost-free multigravity amplitudes

Determine whether the \(\Lambda_3\) high-energy scaling found for ghost-free bimetric theory is retained in ghost-free multigravity theories with multiple massive spin-2 species, or whether additional conversion and exchange channels introduce a lower parameter-dependent strong-coupling scale.

Background

The paper computes all tree-level $2\to2$ amplitudes for ghost-free bimetric theory, which contains one massless and one massive spin-2 mode. The amplitudes exhibit at most $E^6$ growth, corresponding to the characteristic $\Lambda_3$ strong-coupling scale. The authors identify ghost-free multigravity as a natural extension in which several interacting metrics produce one massless and multiple massive spin-2 modes.

With multiple massive species, new processes become possible, including conversion between distinct massive modes, mixed internal exchanges, and additional kinematic thresholds. The unresolved issue is whether these new channels preserve the bimetric $\Lambda_3$ behavior or generate a lower, parameter-dependent strong-coupling scale.