12 problems

Let $SU(N)_k$ Chern–Simons theory have a bulk fusion category of anyonic topological sectors, and let the boundary CFT have local operators and topological defect lines. Bulk–bound…

For $N$ anyons with oscillator confinement, let $\alpha_q$ be the dimensionless quantum statistical parameter. A semiclassical analysis produces eigenvalues that are linear in…

Consider $N$ anyons with oscillator confinement and statistical parameter $\alpha_q$. Their quantum spectrum contains eigenvalues that depend nonlinearly on $\alpha_q$; such eigenv…

Anyons are two-dimensional quantum systems with statistical parameter $\alpha$, whose partially separable Hamiltonian has a pseudo-integrable classical counterpart: it admits const…

String-operator realization conjecture. There exist string operators associated to the simple objects of $Z(\mathcal{C})$ such that, when they are used to define $F$-symbols and…

UMTC–central-charge classification conjecture. Two-dimensional topological phases are labeled by both a UMTC and the number $c_-$ called the chiral central charge.

Anyonic characterization conjecture. Two ground states are in the same phase if and only if their associated anyons behave identically.

Let a path of paths mean a map from $S^2$ to the space of gapped Hamiltonians, and consider the spatially varying Hamiltonian obtained by mapping the plane to $S^2$ so that the ori…

Consider the semilocal Abelian case $N_c=1$, $N_f=\lambda$, and more generally take the Chern--Simons level away from $\lambda=N_f$. Anyonic duality conjecture. The vortex theory i…

Continuity and piecewise-smoothness conjecture. For every finite $N$, the ground-state curve is continuous in $\alpha$ and piecewise smooth, and the number of its smooth pieces gro…

Consider the Bethe roots $y_{jk}$ associated with the highest-energy eigenstate of $\mathcal{H}^{(1)}$ under periodic boundary conditions. The roots occur in complex-conjugate pair…

Haldane's exclusion principle is used to define statistics for many-particle states. In the KYM, applying it to holon eigenstates gives the correct statistics, whereas applying it…