A conjecture on the minimal size of bound states

We conjecture that, in a renormalizable effective quantum field theory where the heaviest stable particle has mass m, there are no bound states with radius below 1/m (Bound State Conjecture). We are motivated by the (scalar) Weak Gravity Conjecture, which can be read as a statement forbidding certain bound states. As we discuss, versions for uncharged particles and their generalizations have shortcomings. This leads us to the suggestion that one...