Integrability of the conformal loop ensemble

06.12.2021 16:15 – 18:15

For 8/3 < κ < 8, the conformal loop ensemble CLEκ is a canonical random ensemble of loops which is conformally invariant in law, and whose loops locally look like Schramm-Loewner evolution with parameter κ. It describes the scaling limits of the Ising model, percolation, and other models. When κ ≤ 4 the loops are simple curves. In this regime we compute the three-point nesting statistic of CLEκ on the sphere, and show it agrees with the imaginary DOZZ formula of Zamolodchikov (2005). We also obtain the expression of the (properly normalized) probability that three points are on the same CLE loop in terms of the DOZZ formula. The analogous quantity for three points on the same cluster was previously conjectured by Delfino and Viti. To our best knowledge our formula has not been predicted in the physics literature. Our arguments depend on couplings of CLE with Liouville quantum gravity and the integrability of Liouville conformal field theory. Based on joint work with Xin Sun.

Lieu

It will be held on zoom:
The zoom link is https://unige.zoom.us/j/62667961409?pwd=THFOKzFIbzhkbnJ1cHdRbnEzSWRFUT09
Meeting ID: 626 6796 1409
Passcode: 540686 Séminaire "Mathématique physique"

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