7 problems

Let $G$ be the physical symmetry group. Let $o_2\in H^2(G,\mathbb{Z}_2)$ be the obstruction to extending the $G$-action from a super modular category to its $\mathbb{Z}_2^f$ modula…

Let $G$ be a symmetry group and let $\mathcal{S}_G$ be a $G$-graded super fusion category. Write $\mathcal{S}_1$ for its trivial grading sector, where $1\in G$ is the trivial eleme…

Let $G$ be the physical symmetry group. A q-type string is called sigma-type when it is conserved modulo $2$ in the fusion rules of surface models. The $H^2(G,\mathbb{Z}_2)$ fermio…

Let $\rho_m$ be a proposed mirror symmetry permutation of the anyons in a topological order. The algorithms of the paper test whether valid mirror symmetry-fractionalization data e…

Let a two-dimensional topological order have anyon excitations with mirror permutation and mirror symmetry-fractionalization data. Let $\{w_a\}$ denote the data introduced through…

Boundary realization conjecture. The anomalous SET phase described by the action in equation may appear as a boundary state of a $(4+1)$-dimensional bulk SPT phase.

Let $\mathcal{C}$ be an $n\times n$ multi-fusion category, and let $D(\mathcal{C})$ denote its associated quantum double. Consider the corresponding Levin–Wen Hamiltonian schema an…