One-loop renormalization of pure Yang-Mills theory with Lorentz violation

The explicit one-loop renormalizability of pure Yang-Mills theory with Lorentz violation is demonstrated. The result is consistent with multiplicative renormalization as the required counterterms are consistent with a single rescaling of the Lorentz-violation parameters. In addition, the resulting beta functions indicate that the $CPT$-even Lorentz-violating terms increase with energy scale in opposition to the asymptotically free gauge coupling and $CPT$-odd terms. The calculations are performed at lowest order in the Lorentz-violating terms as they are assumed small.