A Spin-2 Conjecture on the Swampland

We consider effective theories with massive fields that have spins larger than or equal to two. We conjecture a universal cutoff scale on any such theory that depends on the lightest mass of such fields. This cutoff corresponds to the mass scale of an infinite tower of states, signalling the breakdown of the effective theory. The cutoff can be understood as the Weak Gravity Conjecture applied to the St\"uckelberg gauge field in the mass term of the high spin fields. A strong version of our conjecture applies even if the graviton itself is massive, so to massive gravity. We provide further evidence for the conjecture from string theory.