Conformal welding of quantum disks and multiple SLE: the non-simple case

• 成果类型: Article; Early Access
• 署名作者: Ang, Morris; Holden, Nina; Sun, Xin; Yu, Pu
• 署名单位: University of California System; University of California San Diego; New York University; Peking University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01425-1
• 发表日期: 2025
• 关键词: scaling limits; solution space; gravity; uniqueness; geometry; PERSPECTIVES; CURVES; SYSTEM

摘要

Two-pointed quantum disks with a weight parameter W > 0 is a canonical family of finite-volume random surfaces in Liouville quantum gravity. We prove that the conformal welding of the forested variant of this disk gives a two-pointed quantum disk with an independent SLE kappa for kappa is an element of (4, 8). Furthermore, we show that the conformal welding of multiple forested quantum disks gives a surface arising in Liouville conformal field theory decorated by multiple SLE kappa for kappa is an element of (4, 8), such that the random conformal modulus contains the SLE partition function as a multiplicative factor. In particular, this gives a construction of the multiple SLE kappa associated with any given link pattern. As a corollary, for kappa is an element of(4, 8), we prove the existence of the multiple SLE partition functions, which are smooth functions satisfying a system of PDEs and conformal covariance. This was open for kappa is an element of(6, 8) and N >= 3 prior to our work.