  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.
