• Corpus ID: 233296120

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… 

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