A Species or Weak-Gravity Bound for Large $N$ Gauge Theories Coupled to Gravity

Causality constrains the gravitational interactions of massive higher spin particles in both AdS and flat spacetime. We explore the extent to which these constraints apply to composite particles, explaining why they do not rule out macroscopic objects or hydrogen atoms. However, we find that they do apply to glueballs and mesons in confining large $N$ gauge theories. Assuming such theories contain massive bound states of general spin, we find parametric bounds in $(3+1)$ spacetime dimensions of the form $N\lesssim \frac{M_{Pl}}{\Lambda_{\text{QCD}}}$ relating $N$, the QCD scale, and the Planck scale. We also argue that a stronger bound replacing $\Lambda_{\text{QCD}}$ with the UV cut-off scale may be derived from eikonal scattering in flat spacetime.