  We present a candidate quantum field theory of gravity with dynamical
critical exponent equal to z=3 in the UV. (As in condensed matter systems, z
measures the degree of anisotropy between space and time.) This theory, which
at short distances describes interacting nonrelativistic gravitons, is
power-counting renormalizable in 3+1 dimensions. When restricted to satisfy the
condition of detailed balance, this theory is intimately related to
topologically massive gravity in three dimensions, and the geometry of the
Cotton tensor. At long distances, this theory flows naturally to the
relativistic value z=1, and could therefore serve as a possible candidate for a
UV completion of Einstein's general relativity or an infrared modification
thereof. The effective speed of light, the Newton constant and the cosmological
constant all emerge from relevant deformations of the deeply nonrelativistic
z=3 theory at short distances.
