Closure of the algebra of constraints for a nonprojectable Hořava model

We perform the Hamiltonian analysis for a nonprojectable Hořava model whose potential is composed of $R$ and $R^2$ terms. We show that Dirac’s algorithm for the preservation of the constraints can be done in a closed way, hence the algebra of constraints for this model is consistent. The model has an extra, odd, scalar mode whose decoupling limit can be seen in a linear-order perturbative analysis on weakly varying backgrounds. Although our results for this model point in favor of the consistency of the Hořava theory, the validity of the full nonprojectable theory still remains unanswered.

Figure 1

(a) A typical flow of $V$. (b) If a zero of $V$ was excluded from $\Sigma$ then in the neighborhood of the zero there could be a set of loops disconnected to $\Sigma$.