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arXiv · 2603.28161

Boundary four-point connectivities of conformal loop ensembles

Gefei Cai
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Abstract

We derive the boundary four-point Green's functions for conformal loop ensembles (CLE) with $κ\in(4,8)$. Specializing to $κ=6$ and $κ=16/3$, we establish the exact formulas for the boundary four-point connectivities in critical Bernoulli percolation and the FK-Ising model conjectured by Gori-Viti (2017, 2018). In particular, we identify a logarithmic singularity in the critical FK-Ising model. Our approach also applies to the one-bulk and two-boundary connectivities of CLE, thereby extending the factorization formula of Beliaev-Izyurov (2012) to all $κ\in(4,8)$.

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Gefei Cai. 2026-04-06. Boundary four-point connectivities of conformal loop ensembles. https://arxiv.org/abs/2603.28161

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