Tensor network approach to electromagnetic duality in (3+1)d topological gauge models

Understand

Given the Hamiltonian realisation of a topological (3+1)d gauge theory with finite group $G$, we consider a family of tensor network representations of its ground state subspace.

• This family is indexed by gapped boundary conditions encoded into module 2-categories over the input spherical fusion 2-category.
• Individual tensors are characterised by symmetry conditions with respect to non-local operators acting on entanglement degrees of freedom.
• In the case of Dirichlet and Neumann boundary conditions, we show that the symmetry operators form the fusion 2-categories $\mathsf{2Vec}_G$ of $G$-graded 2-vector spaces and $\mathsf{2Rep}(G)$ of 2-representations of $G$, respectively.