  Entanglement is assuming a central role in modern quantum many-body physics.
Yet, for lattice gauge theories its certification remains extremely
challenging. A key difficulty stems from the local gauge constraints underlying
the gauge theory, which separate the full Hilbert space into a direct sum of
subspaces characterized by different superselection rules. In this work, we
develop the theoretical framework of entanglement witnessing for lattice gauge
theories that takes this subtlety into account. We illustrate the concept at
the example of a $\mathrm{U}(1)$ lattice gauge theory in 2+1 dimensions,
without and with dynamical fermionic matter. As this framework circumvents
costly state tomography, it opens the door to resource-efficient certification
of entanglement in theoretical studies as well as in laboratory quantum
simulations of gauge theories.
