  The partition function of three dimensional gravity in the quantum level,
where the AdS radius $\ell$ is Planck scale, is dual to the Ising model when
the central charge $c=3\ell/2G$ is $1/2$. 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. Since every value of $c < 1$
corresponding to two values of $\kappa$, then it 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.

High Energy Physics - Theory