Petr Hořava proposes a quantum field theory of gravity with dynamical critical exponent z = 3 in the ultraviolet (UV). This theory, which describes interacting nonrelativistic gravitons at short distances, is power-counting renormalizable in 3+1 dimensions. When restricted to satisfy the detailed balance condition, it is related to topological gravity in three dimensions and the geometry of the Cotton tensor. At long distances, the theory flows to the relativistic value z = 1, potentially serving as a UV completion of Einstein's general relativity or an infrared modification. The effective speed of light, Newton constant, and cosmological constant emerge from relevant deformations of the nonrelativistic z = 3 theory. The theory is constructed using anisotropic scaling with z = 3, and the fields include the spatial metric, lapse, and shift variables. The action is invariant under foliation-preserving diffeomorphisms and includes a kinetic term and potential term. The potential term is constrained by the detailed balance condition, leading to a theory related to the Cotton tensor. The theory exhibits anisotropic Weyl invariance at λ = 1/3 and flows to z = 1 in the infrared. The theory is power-counting renormalizable in 3+1 dimensions and has applications in condensed matter physics and quantum critical phenomena.Petr Hořava proposes a quantum field theory of gravity with dynamical critical exponent z = 3 in the ultraviolet (UV). This theory, which describes interacting nonrelativistic gravitons at short distances, is power-counting renormalizable in 3+1 dimensions. When restricted to satisfy the detailed balance condition, it is related to topological gravity in three dimensions and the geometry of the Cotton tensor. At long distances, the theory flows to the relativistic value z = 1, potentially serving as a UV completion of Einstein's general relativity or an infrared modification. The effective speed of light, Newton constant, and cosmological constant emerge from relevant deformations of the nonrelativistic z = 3 theory. The theory is constructed using anisotropic scaling with z = 3, and the fields include the spatial metric, lapse, and shift variables. The action is invariant under foliation-preserving diffeomorphisms and includes a kinetic term and potential term. The potential term is constrained by the detailed balance condition, leading to a theory related to the Cotton tensor. The theory exhibits anisotropic Weyl invariance at λ = 1/3 and flows to z = 1 in the infrared. The theory is power-counting renormalizable in 3+1 dimensions and has applications in condensed matter physics and quantum critical phenomena.