Bulk-boundary correspondence conjecture for two-dimensional Hamiltonians

Let a two-dimensional Hamiltonian on a spin system satisfy the assumptions denoted by

$$through$$

, and let $\mathfrak A$ be its net of boundary algebras. Write $\mathsf{DHR}(\mathfrak A)$ for the category of DHR bimodules of $\mathfrak A$, equipped with its canonical braiding. Bulk-boundary correspondence conjecture. For 2D Hamiltonians on a spin system satisfying the stated assumptions, the bulk topological order is the braided DHR category of bimodules of the net of boundary algebras. The claim identifies bulk topological excitations with the braided DHR bimodule category of the boundary net; the preceding theorem establishes a canonical braiding under weak algebraic Haag duality, but the conjectural identification itself is not resolved in the supplied text.