## 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 SLE_{4}. 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’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.

Original language | English (US) |
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Pages (from-to) | 1229-1254 |

Number of pages | 26 |

Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |

Volume | 57 |

Issue number | 3 |

DOIs | |

State | Published - Aug 2021 |

## Keywords

- Conformal welding
- Critical Liouville quantum gravity
- Quantum zipper
- Schramm–Loewner evolutions

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty