9 problems

Massless RG-flow conjecture. This positive solution corresponds to the existing massless renormalization-group flow. Further studies using other methods are needed to confirm this…

Positive-dimension unitarity conjecture. If

Orbifold quantum-dimension conjecture. Every irreducible ordinary $\mathcal{H}(3)^{S_3}$-module $M$ appears in the decomposition of a $g$-twisted $\mathcal{H}(3)$-module for some…

Let $V$ be a simple vertex operator algebra and a semisimple $H$-module vertex operator algebra. Let $V^H$ be the fixed-point vertex operator algebra, let $I$ index the irreducible…

Quantum-dimension criterion. The anyon $a$ is braiding universal if and only if $\dim(a)^2$ is not an integer.

Let $V$ be a vertex operator algebra with only finitely many irreducible modules, and let $\operatorname{Irr}(V)$ denote the set of irreducible $V$-modules. For…

Property F conjecture. The images $\rho_{n,x}(B_n)$ in $U(V_{n,x})$ are all finite subgroups if and only if $d_x^2\in\mathbb{Z}$. This conjecture relates finite braid-group images…

Let $x$ be an anyon with quantum dimension $d_x$, and call $x$ braiding universal when its braid-group representations provide universal anyonic quantum computation. Braiding-unive…

Quantum-dimension conjecture. For every $\chi\in\operatorname{Irr}(G)$,