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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Anchored random clusters and SLE excursions

  • Federico Camia1,2
  • Valentino F. Foit1,2
  • Rongvoram Nivesvivat1
  1. 1New York University Abu Dhabi
  2. 2New York University
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Abstract

A bstract : We provide a pedagogical review of CFT techniques to compute certain Schramm-Loewner Evolution (SLE) observables in the upper half-plane. The approach relies on the ability to express the observables as bulk-boundary correlation functions that involve degenerate boundary operators and, therefore, obey certain differential equations. In particular, we recover Schramm’s left-passage probability for SLE, the SLE Green’s functions, and the generalized densities of “anchored” critical percolation clusters first obtained by Kleban, Simmons, and Ziff. We also obtain new formulas corresponding to the densities of pivotal points between critical Fortuin-Kasteleyn (FK) clusters.

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Cite

BibTeXRIS
BibTeX
@article{camia2026anchored,
  title = {{Anchored random clusters and SLE excursions}},
  author = {Federico Camia and Valentino F. Foit and Rongvoram Nivesvivat},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = oct,
  doi = {10.1007/jhep10(2026)015},
  url = {https://link.springer.com/10.1007/JHEP10(2026)015},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Anchored random clusters and SLE excursions
AU  - Federico Camia
AU  - Valentino F. Foit
AU  - Rongvoram Nivesvivat
PY  - 2026
DA  - 2026/10/01
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep10(2026)015
UR  - https://link.springer.com/10.1007/JHEP10(2026)015
AB  - A bstract : We provide a pedagogical review of CFT techniques to compute certain Schramm-Loewner Evolution (SLE) observables in the upper half-plane. The approach relies on the ability to express the observables as bulk-boundary correlation functions that involve degenerate boundary operators and, therefore, obey certain differential equations. In particular, we recover Schramm’s left-passage probability for SLE, the SLE Green’s functions, and the generalized densities of “anchored” critical percolation clusters first obtained by Kleban, Simmons, and Ziff. We also obtain new formulas corresponding to the densities of pivotal points between critical Fortuin-Kasteleyn (FK) clusters.
SN  - 1029-8479
ER  -