On the consistency of the Horava Theory

Abstract

With the goal of giving evidence for the theoretical consistency of the Hořava Theory, we perform a Hamiltonian analysis on a classical model suitable for analyzing its effective dynamics at large distances. The model is the lowest-order truncation of the Hořava Theory with the detailed-balance condition. We consider the pure gravitational theory without matter sources. The model has the same potential term of general relativity, but the kinetic term is modified by the inclusion of an arbitrary coupling constant λ. Since this constant breaks the general covariance under space-time diffeomorphisms, it is believed that arbitrary values of λ deviate the model from general relativity. We show that this model is not a deviation at all, instead it is completely equivalent to general relativity in a particular partial gauge fixing for it. In doing this, we clarify the role of a second-class constraint of the model. There have been a lot of interest about Hořava’s proposal of a new theory of gravity which in principle has a renormalizable quantum version [1] (an important part of the conceptual and technical basis was previously developed in Ref. [2]). To build such a theory, Hořava has proposed to abandon the principle of space-time relativity as a fundamental symmetry of nature, reducing the freedom to perform coordinate transformations to those transformations that preserve some preferred universal time-like foliation. The advantage of this scheme is that one can include higher spatial-derivative terms in the Lagrangian that render the theory renormalizable. According to Hořava’s point of view, jorgebellorin@usb.ve arestu@usb.ve