Renormalization of the nonprojectable Horava theory

We present the proof of renormalization of the Horava theory, in the nonprojectable version. We obtain a form of the quantum action that exhibits a manifest BRST-symmetry structure. Previous analysis has shown that the divergences produced by irregular loops cancel completely between them. The remaining divergences are local. The renormalization is achieved by using the approach developed by Barvinsky et al. with the background-field formalism.