Cancellation of divergences in the nonprojectable Hor?ava theory

We perform an analysis of the ultraviolet divergences of the quantum nonprojectable Hor ˇava gravity. We work the quantum-field theory directly in the Hamiltonian formalism provided by the Batalin-Fradkin-Vilkovisky quantization. In this way the second-class constraints can be incorporated into the quantization. A known local gauge-fixing condition leads to a local canonical Lagrangian. Although the canonical fields acquire regular propagators, irregular propagators persist dangerous subdivergences. We show that all these loops cancel exactly between them due to a perfect matching between the propagators and vertices of the fields and ghosts forming the loops. The rest of the divergences behave similarly to the projectable theory, they can be removed by local counterterms. This result points to the renormalization of the nonprojectable Hor ˇava theory.