Proposal for a CFT interpretation of Watts' differential equation for percolation
Abstract
G. M. T. Watts derived that in two dimensional critical percolation the crossing probability Pihv satisfies a fifth order differential equation which includes another one of third order whose independent solutions describe the physically relevant quantities 1, Pih, Pihv. We will show that this differential equation can be derived from a level three null vector condition of a rational c=-24 CFT and motivate how this solution may be fitted into known properties of percolation.
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