Renormalization of gauge theories and asymptotic freedom of Horava-Lifshitz gravity

Using the background-field method we demonstrate the Becchi-Rouet-Stora-Tyutin (BRST) structure of counterterms in a broad class of gauge theories. Put simply, we show that gauge invariance is preserved by renormalization in local gauge field theories whenever they admit a sensible background-field formulation and anomaly-free path integral measure. This class encompasses Yang--Mills theories and relativistic gravity, including both renormalizable and non-renormalizable (effective) theories. Our results also hold for non-relativistic models such as Yang--Mills theories with anisotropic scaling or Horava gravity. They strengthen and generalize the existing results in the literature concerning the renormalization of gauge systems. We illustrate our general approach with several explicit examples and show asymptotic freedom of the (2+1)-dimensional Horava-Lifshitz gravity.