Abstract
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 κ. In fact, SLE depends on the parameter κ, which controls the diffusion of the Brownian motion. Each value of c < 1 corresponds to two values of κ, 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.
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