@article{d95fb0be7cdc49fe9a93de08e9f9a5ca,

title = "Conformal welding for critical Liouville quantum gravity",

abstract = "Consider two critical Liouville quantum gravity surfaces (i.e., γ-LQG for γ = 2), each with the topology of H and with infinite boundary length. We prove that there a.s. exists a conformal welding of the two surfaces, when the boundaries are identified according to quantum boundary length. This results in a critical LQG surface decorated by an independent SLE4. Combined with the proof of uniqueness for such a welding, recently established by McEnteggart, Miller, and Qian (2018), this shows that the welding operation is well-defined. Our result is a critical analogue of Sheffield{\textquoteright}s quantum gravity zipper theorem (2016), which shows that a similar conformal welding for subcritical LQG (i.e., γ-LQG for γ ∈ (0,2)) is well-defined.",

keywords = "Conformal welding, Critical Liouville quantum gravity, Quantum zipper, Schramm–Loewner evolutions",

author = "Nina Holden and Ellen Powell",

note = "Funding Information: N. Holden acknowledges support from Dr. Max R{\"o}ssler, the Walter Haefner Foundation, and the ETH Z{\"u}rich Foundation. E. Powell is supported by the SNF grant #175505. Both authors would like to express their thanks to Juhan Aru, for his valuable input towards the initiation and strategy of this project, and for numerous helpful discussions. They also thank an anonymous referee for his or her careful reading of the paper and for helpful comments. Funding Information: N. Holden acknowledges support from Dr. Max R?ssler, the Walter Haefner Foundation, and the ETH Z?rich Foundation. E. Powell is supported by the SNF grant #175505. Both authors would like to express their thanks to Juhan Aru, for his valuable input towards the initiation and strategy of this project, and for numerous helpful discussions. They also thank an anonymous referee for his or her careful reading of the paper and for helpful comments. Publisher Copyright: {\textcopyright} Association des Publications de l{\textquoteright}Institut Henri Poincar{\'e}, 2021.",

year = "2021",

month = aug,

doi = "10.1214/20-AIHP1116",

language = "English (US)",

volume = "57",

pages = "1229--1254",

journal = "Annales de l'institut Henri Poincare (B) Probability and Statistics",

issn = "0246-0203",

publisher = "Institute of Mathematical Statistics",

number = "3",

}