6 problems

Let $M$ be a combinatorial map and $W$ a choice of loop weights, and write $Z_{M,W}$ for the associated loop-model correlation function. Assume the critical limit exists. The corre…

Let an $n$-point function of diagonal and non-diagonal fields lie on a Riemann surface of genus $g$. In each channel, consider conformal-bootstrap spectra containing all allowed no…

Consider an $n$-point function of diagonal and non-diagonal fields on a Riemann surface of genus $g$. Let $\mathcal{M}^c_{g,n}(r_i)$ denote the set of weakly connected maps with th…

Let $\mathcal{M}_{0,4}(r_1,r_2,r_3,r_4)$ be the set of maps with the specified vertex data, and order signatures componentwise: $\sigma ot greater than or equal tosigma'$ when…

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…