  We compute the one-loop effective action of the Horava theory, in its
nonprojectable formulation. We take the quantization of the (2+1)-dimensional
theory in the Batalin-Fradkin-Vilkovisky formalism, and comment on the
extension to the (3+1) case. The second-class constraints and the appropriate
gauge-fixing condition are included in the quantization. The ghost fields
associated with the second-class constraints can be used to get the integrated
form of the effective action, which has the form of a Berezinian. We show that
all irregular loops cancel between them in the effective action. The key for
the cancellation is the role of the ghosts associated with the second-class
constraints. These ghosts form irregular loops that enter in the denominator of
the Berezinian, eliminating the irregular loops of the bosonic nonghost sector.
Irregular loops produce dangerous divergences; hence their cancellation is an
essential step for the consistency of the theory. The cancellation of this kind
of divergences is in agreement with the previous analysis done on the (2+1)
quantum canonical Lagrangian and its Feynman diagrams.
