6 problems

Three-dimensional derivation conjecture. The Liouville CFT partition function of $\Sigma$ can be derived from quantities associated with $M$. This conjecture proposes a three-dimen…

Contour-deformation conjecture. Physicists conjecture that, for a general bootstrap formula, the integration contour should be the spectrum line $Q+iP$ together with small circles…

Let $Q$, $\beta$, $\mu$, $\mu_\partial$, $P$, $q$, $G$, $U_{\rm FZZ}$, $\eta$, and $H$ be the quantities in the annulus Liouville CFT bootstrap formula. For $\mu\;\geqslant\; 0$,…

Consider an annulus represented as a cylinder of length $\pi\tau$ and radius $1$. Set $q=e^{-2\pi\tau}$, and let $\mathcal{Z}_{\mathrm{Annulus}}$ denote the no-insertion-point part…

Let $V^1$ be the unit-volume Liouville random measure defined from the Liouville measure by normalizing its total mass to $1$, under the integrability assumptions stated in the sur…

Let $coperatorname{Vol}$ denote the total mass of the Liouville measure, and consider the corresponding unit-volume Liouville measure on a sphere-like manifold. Sheffield's unit ar…