Proposal for a CFT interpretation of Watts' differential equation for percolation

TL;DR

This paper connects Watts' differential equation for 2D critical percolation crossing probabilities to a rational conformal field theory with c=-24, providing a new theoretical interpretation.

Contribution

It introduces a CFT framework with a level three null vector condition to derive Watts' differential equation for percolation.

Findings

Derivation of Watts' equation from c=-24 CFT

Identification of solutions with physical percolation quantities

Proposed fit of CFT solutions to known percolation properties

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.