  We present a one loop calculation in the context of Horava-Lifshitz gravity.
Due to the complexity of the calculation in the full theory we focus here on
the study of a toy model, namely the conformal reduction of the z=2 projectable
theory in 2+1 dimensions. For this value of the dimension there are no
gravitons, hence the conformal mode is the only physical degree of freedom, and
thus we expect our toy model to lead to qualitatively correct answers regarding
the perturbative renormalization of the full theory. We find that Newton's
constant (dimensionless in Horava-Lifshitz gravity) is asymptotically free.
However, the DeWitt supermetric approaches its Weyl invariant form with the
same speed and the effective interaction coupling remains constant along the
flow. In other words, the would-be asymptotic freedom associated to the running
Newton's constant is exactly balanced by the strong coupling of the scalar mode
as the Weyl invariant limit is approached. We conclude that in such model the
UV limit is singular at one loop order, and we argue that a similar phenomenon
can be expected in the full theory, even in higher dimensions.
