Causality Constraints in Large $N$ QCD Coupled to Gravity

TL;DR

This paper explores how causality constraints in large N QCD coupled to gravity imply the necessity of stringy features or additional higher spin states below the Planck scale, revealing deep connections between confinement, gravity, and string theory.

Contribution

It demonstrates that resolving causality issues in large N QCD coupled to gravity requires either mixing with QCD states or string-like features in the UV completion, with implications for the string scale.

Findings

Causality conflicts arise with metastable higher spin states coupled to gravity.

QCD sector mixing can resolve causality issues, requiring all particles to interact with glueballs.

A stringy UV completion is implied for weakly coupled gravity, with an upper bound on the string scale.

Abstract

Confining gauge theories contain glueballs and mesons with arbitrary spin, and these particles become metastable at large $N$. However, metastable higher spin particles, when coupled to gravity, are in conflict with causality. This tension can be avoided only if the gravitational interaction is accompanied by interactions involving other higher spin states well below the Planck scale $M_{\rm pl}$. These higher spin states can come from either the QCD sector or the gravity sector, but both these resolutions have some surprising implications. For example, QCD states can resolve the problem since there is a non-trivial mixing between the QCD sector and the gravity sector, requiring all particles to interact with glueballs at tree-level. If gravity sector states restore causality, any weakly coupled UV completion of the gravity-sector must have many stringy features, with an upper bound on the string scale. Under the assumption that gravity is weakly coupled, both scenarios imply that the theory has a stringy description above $N\gtrsim \frac{M_{\rm pl}}{\Lambda_{\rm QCD}}$, where $\Lambda_{\rm QCD}$ is the confinement scale.