Strong coupling quantum Einstein gravity at a $z=2$ Lifshitz point

We solve a renormalized Wheeler-DeWitt equation for Einstein gravity in $D+1$ dimensions with $D=\mathrm{\text{odd}}$ in the strong coupling limit, which is expected to be suited to probe quantum geometry at short distances, in order to test Hořava’s idea that quantum gravity at short distances will be described by a nonrelativistic system with dynamical critical exponent $z>1$. Our results support the idea and show that the Wheeler-DeWitt equation possesses a solution associated with a $z=2$ Lifshitz point but no other $z>2$ solutions to leading order of the strong coupling expansion.