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

## TL;DR

This paper investigates how causality constraints limit the properties of bound states in large N gauge theories coupled to gravity, deriving bounds on N based on the QCD and Planck scales.

## Contribution

It extends causality bounds to composite particles in large N gauge theories, establishing a new relation between N, the QCD scale, and the Planck scale.

## Key findings

- Causality constrains glueballs and mesons in large N theories.
- Derived bounds relate N to the ratio of Planck and QCD scales.
- Proposed stronger bounds from flat spacetime scattering analysis.

## Abstract

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.