  The Lagrangian for a non-abelian gauge theory with an $SU(N_{\! c})$ symmetry
and a linear covariant gauge fixing is constructed in eight dimensions. The
renormalization group functions are computed at one loop with the special cases
of $N_{\! c}$ $=$ $2$ and $3$ treated separately. By computing the critical
exponents derived from these in the large $N_{\! f}$ expansion at the
Wilson-Fisher fixed point it is shown that the Lagrangian is in the same
universality class as the two dimensional non-abelian Thirring model and
Quantum Chromodynamics (QCD). As the eight dimensional Lagrangian contains new
quartic gluon operators not present in four dimensional QCD, we compute in
parallel the mixing matrix of four dimensional dimension $8$ operators in pure
Yang-Mills theory.
