12 problems

Let $\mathcal{B}$ be an anyon model, let $\mathcal{M}_{\mathcal{B}}$ be the moduli space of gapped systems with intrinsic topological order $\mathcal{B}$, and let…

Multi-qubit double-braiding universality conjecture. The universality of double-braidings should also hold for the multi-qubit case, that is, for spaces of more than three anyons.

In a graph-braided anyon model, charge conservation for a subset of particles imposes diagonality conditions on the corresponding braiding exchange operator in a basis where that s…

Consider the trijunction $\Gamma_T$ and the simplified anyon models whose symbols have at most four labels. Let $N_0(\Gamma_T)$ denote the particle number beyond which all consiste…

Let $\Gamma$ be a graph, and let $N_0(\Gamma)$ be a number such that the consistency relations for all particle numbers $N>N_0(\Gamma)$ are satisfied by solutions of the consistenc…

A graph-braided anyon fusion model assigns braiding exchange operators to graph-braid generators and satisfies polygon equations expressing compatibility between fusion and braidin…

Property F conjecture. An anyon $X$ is braiding universal if and only if

Let $\mathcal{V}$ be a vertex operator algebra with symmetry group $G$, and let $G_0$ be the identity component of $G$. Let $\operatorname{Rep}(\mathcal{V})$ denote the representat…

An anyon model is a unitary modular tensor category, and a chiral conformal field theory may be mathematically described by a vertex operator algebra or a local conformal net. The…

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

Let $V^{1111}_0$ denote the qubit model shown in the paper's Figure 1, and allow measurements of total charges of metaplectic anyons. A model is Ising like if its braidings and the…

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…