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 Pi_hv satisfies a fifth order differential equation which includes another one of third order whose independent solutions describe the physically relevant quantities 1, Pi_h, Pi_hv. 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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References in corpus (2)

• The Loewner equation: maps and shapes
• Critical percolation in the plane

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