Proposal for a conformal field theory interpretation of Watts’ differential equation for percolation

G M T Watts established that in two-dimensional critical percolation the crossing probability Π hv satisfies a fifth-order differential equation which includes another one of third order whose independent solutions describe the physically relevant quantities 1,Π h ,Π hv . We will show that this differential equation can be derived from a level three null vector condition for a rational c = −24 conformal field theory and motivate how this solution may be fitted into known properties of percolation.