The bulk energy four-point function in percolation and self-avoiding walk CFTs is non-zero at c=0, driven by coupling to a rank-3 Jordan block associated with the second energy operator.
A conformal bootstrap approach to critical percolation in two dimensions
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abstract
We study four-point functions of critical percolation in two dimensions, and more generally of the Potts model. We propose an exact ansatz for the spectrum: an infinite, discrete and non-diagonal combination of representations of the Virasoro algebra. Based on this ansatz, we compute four-point functions using a numerical conformal bootstrap approach. The results agree with Monte-Carlo computations of connectivities of random clusters.
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Logarithmic operators in $c=0$ bulk CFTs
The bulk energy four-point function in percolation and self-avoiding walk CFTs is non-zero at c=0, driven by coupling to a rank-3 Jordan block associated with the second energy operator.