# Safe Glueballs and Baryons

## TL;DR

This paper investigates the existence of a UV fixed point in a non-Abelian gauge theory with many fermions, analyzing operator dimensions and their implications for the theory's consistency.

## Contribution

It provides a first-order $1/N_f$ analysis of operator anomalous dimensions at the fixed point, revealing potential unitarity violations for glueball operators.

## Key findings

- Glueball operator anomalous dimension violates unitarity bound at fixed point.
- Baryon operators have small anomalous dimensions within unitarity bounds.
- The existence of the fixed point is uncertain due to unitarity considerations.

## Abstract

We consider a non-Abelian gauge theory with $N_f$ fermions and discuss the possible existence of a non-trivial UV fixed point at large $N_f$. Specifically, we study the anomalous dimension of the (rescaled) glueball operator $\text{Tr}\ F^2$ to first order in $1/N_f$ by relating it to the derivative of the beta function at the fixed point. At the fixed point the anomalous dimension violates its unitarity bound and so the (rescaled) glueball operator is either decoupled or the fixed point does not exist. We also study the anomalous dimensions of the two spin-$1/2$ baryon operators to first order in $1/N_f$ for an $SU(3)$ gauge theory with fundamental fermions and find them to be relatively small and well within their associated unitarity bounds.