Cancellation of divergences in the nonprojectable Horava theory

We perform an analysis of the ultraviolet divergences of the quantum nonprojectable Horava 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 to the quantization. A known local gauge-fixing condition leads to a local canonical Lagrangian. Although the canonical fields acquire regular propagators, irregular propagators persist for the field associated to the measure of the second-class constraints. Loops can be formed with the irregular propagators producing potentially 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 divergences behaves similiarly to the projectable theory, they can be removed by local counterterms. This result points to the renormalization of the nonprojectable Horava theory.