BRST symmetry and unitarity of the Hořava theory

We present an analysis on the Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformations of Ho\ifmmode \check{r}\else \v{r}\fi{}ava theory under Batalin-Fradkin-Vilkovisky quantization, both in nonprojectable and projectable cases. obtain that BRST are intimately related to a particular spatial diffeomorphism along one ghost vector fields. show explicitly invariance quantum action nilpotence transformations, using this largely. The is verified whole phase space, inside outside constrained surface. When restricted surface, completely local. consistency fundamental feature field theory, specially for renormalization. BFV quantization independent chosen gauge-fixing condition. This allows us study unitarity covering gauge required prove that, if solution lapse function exists, then established.