Gapped Boundary Theory of the Twisted Gauge Theory Model of Three-Dimensional Topological Orders

Understand

We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries.

• We achieve this by systematically constructing the boundary Hamiltonians that are compatible with the bulk Hamoltonian.
• Given the bulk Hamiltonian defined by a gauge group $G$ and a four-cocycle $\omega$ in the fourth cohomology group of $G$ over $U(1)$, a boundary Hamiltonian can be defined by a subgroup $K$ of $G$ and a three-cochain $\alpha$ in the third cochain group of $K$ over $U(1)$.
• The boundary Hamiltonian to be constructed must be gapped and invariant under the topological renormalization group flow (via Pachner moves), leading to a generalized Frobenius condition.