6 problems

On the honeycomb lattice, an $O(N)$ configuration $c$ is a family of disjoint finite self-avoiding loops. If $l(c)$ is the number of loops and $L(c)$ their total length, configurat…

Consider the conjectured spectrum of the two-dimensional $O(n)$ conformal field theory, including the field $V^{[]}_{(2,1)}$ and the singlet-sector solution space…

Let $V^{\lambda_i}_{(r_i,s_i)}$ be fields in the two-dimensional $O(n)$ conformal field theory, and let $\{T_k\}_k$ be a basis of four-point invariants. Writing a four-point functi…

Fix $n\in[0,2]$ and consider the loop $O(n)$ model with an interface between boundary points $a$ and $b$. Smirnov's O(n)-model interface conjecture. For $z=1/\sqrt{2+\sqrt{2-n}}$,…

Positivity-threshold conjecture. $\rho\leq\rho_c$, where

Kager–Nienhuis conjecture. For $N\in[0,2]$, the model has conformally invariant scaling limits for