5 problems

Let $Q=b+b^{-1}$, and let $\alpha_1,\alpha_2,\alpha_3,\alpha_4,\alpha_{23}$ be complex Liouville momenta. The fusion coefficients are denoted by…

Let $\mathbb S$ be the contour of intermediate Liouville momenta, and let ${{\mathcal F}}^s_{\alpha_{21}}$ and ${{\mathcal F}}^t_{\alpha_{32}}$ denote the s- and t-channel conformal…

Liouville completeness conjecture. Liouville conformal blocks form a complete basis with respect to the inner product above. This is the second mathematical gap in the rigorous def…

Let $c\geq 25$ and consider the inner product on conformal blocks … where $Z_{bc}$ is the ghost partition function and $Z_{26-c}$ is the timelike Liouville correlation function wit…

Let $\gamma$ and $Q$ be the Liouville parameters, with $\beta\in(\frac{\gamma}{2},Q)$ and $\mu,\mu_1,\mu_2>0$. For $i=1,2$, define $\sigma_i$ by … Let $R(\beta,\sigma_1,\sigma_2)$…