In the talk, I will explain a quantum definition of the butterfly effect and how it can be related to fractional statistics. This connection comes from the characterization of the butterfly effect by the out-of-time-order-correlator proposed recently. I will show that this correlator in (1+1)-d rational conformal field theories is intrinsically related it to the fractional statistics in (2+1)-d.

The talk is based on arXiv: 1602.06543.