Integrability of SLE via conformal welding of random surfaces
@inproceedings{Ang2021IntegrabilityOS, title={Integrability of SLE via conformal welding of random surfaces}, author={Morris Ang and Nina Holden and Xin Sun}, year={2021} }
We demonstrate how to obtain integrability results for the Schramm-Loewner evolution (SLE) from Liouville conformal field theory (LCFT) and the mating-of-trees framework for Liouville quantum gravity (LQG). In particular, we prove an exact formula for the law of a conformal derivative of a classical variant of SLE called SLEκ(ρ−; ρ+). Moreover, we prove that the SLE loop measure constructed by Zhan (2020) arises naturally from the conformal welding of two quantum disks in LQG. Our proofs are…
8 Citations
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