From Percolation to Logarithmic Conformal Field Theory

TL;DR

This paper introduces a new logarithmic conformal field theory at c=0 derived from minimal models, providing a consistent framework for percolation crossing probabilities and fusion rules, and highlighting differences from other c=0 theories.

Contribution

It presents the smallest deformation of the minimal model M(2,3) leading to a consistent logarithmic CFT at c=0 with a new method for computing fusion rules.

Findings

Derived a consistent logarithmic CFT at c=0 from minimal models.

Provided a simple recipe for fusion rule computation.

Highlighted differences from other c=0 logarithmic CFTs.

Abstract

The smallest deformation of the minimal model M(2,3) that can accommodate Cardy's derivation of the percolation crossing probability is presented. It is shown that this leads to a consistent logarithmic conformal field theory at c=0. A simple recipe for computing the associated fusion rules is given. The differences between this theory and the other recently proposed c=0 logarithmic conformal field theories are underlined. The discussion also emphasises the existence of invariant logarithmic couplings that generalise Gurarie's anomaly number.