  The partition function of three dimensional gravity in the quantum regime is
dual to the Ising model when the central charge $c=1/2$. Mathematically, we
show that the three dimensional gravity can be described by Schramm-Loewner
Evolution(SLE) with certain $\kappa$. In fact, SLE depends on the parameter
$\kappa$ which controls the diffusion of the Brownian motion. Each value of $c
< 1$ corresponds to two values of $\kappa$, which may hint that the three
dimensional gravity has two different phases at certain central charge c.
Moreover, phase transition is also discussed in AdS and Ising model.
