  The Horava theory depends on several coupling constants. The kinetic term of
its Lagrangian depends on one dimensionless coupling constant lambda. For the
particular value lambda = 1/3 the kinetic term becomes conformal invariant,
although the full Lagrangian does not have this symmetry. For any value of
lambda the nonprojectable version of the theory has second-class constraints
which play a central role in the process of quantization. Here we study the
complete nonprojectable theory, including the Blas-Pujolas-Sibiryakov
interacting terms, at the kinetic-conformal point lambda = 1/3. The generic
counting of degrees of freedom indicates that this theory propagates the same
physical degrees of freedom of General Relativity. We analyze this point
rigorously taking into account all the z=1,2,3 terms that contribute to the
action describing quadratic perturbations around the Minkowski spacetime. We
show that the constraints of the theory and equations determining the Lagrange
multipliers are strongly elliptic partial differential equations, an essential
condition for a constrained phase-space structure in field theory. We show how
their solutions lead to the two independent tensorial physical modes propagated
by the theory. We also obtain the reduced Hamiltonian. These arguments
strengthen the consistency of the theory. We find the restrictions on the space
of coupling constants to ensure the positiveness of the reduced Hamiltonian. We
obtain the propagator of the physical modes, showing that there are not ghosts
and that the propagator effectively acquires the z=3 scaling for all physical
degrees of freedom at the high energy regime. By evaluating the superficial
degree of divergence, taking into account the second-class constraints, we show
that the theory is power-counting renormalizable. ...
