Equivalence of metric gluing and conformal welding in $\gamma$-Liouville quantum gravity for $\gamma \in (0,2)$

Liam Hughes, Jason Miller

We consider the $\gamma$-Liouville quantum gravity (LQG) model for $\gamma \in (0,2)$, formally described by $e^{\gamma h}$ where $h$ is a Gaussian free field on a planar domain $D$. Sheffield show…