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The entanglement entropy associated to a region of space plays an important role in black
hole thermodynamics, quantum information theory, condensed matter theory and the AdS/CFT
correspondence. In a gauge theory the entanglement entropy acquires qualitatively new
features, and its definition requires introducing edge states of the kind that appear in
three-dimensional quantum gravity and the quantum Hall effect.
The edge states transform nontrivially under the gauge group of the boundary, which
constrains the form of the reduced density matrix. I will illustrate this explicitly using
a lattice regulator, and show that the gauge symmetry leads to a splitting of the
entanglement entropy into bulk and boundary parts. Although the considerations are very
general, I will illustrate them with three examples: Yang-Mills theory in two dimensions,
the toric code, and lattice Yang-Mills at strong coupling.
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