Conformal welding for critical Liouville quantum gravity

Nina Holden, Ellen Powell

Research output: Contribution to journalArticlepeer-review


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’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 languageEnglish (US)
Pages (from-to)1229-1254
Number of pages26
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number3
StatePublished - Aug 2021


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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