  Entanglement entropy has proven to be an extremely useful concept in quantum
field theory. Gauge theories are of particular interest, but for these systems
the entanglement entropy is not clearly defined because the physical Hilbert
space does not factor as a tensor product according to regions of space. Here
we review a definition of entanglement entropy that applies to abelian and
nonabelian lattice gauge theories. This entanglement entropy is obtained by
embedding the physical Hilbert space into a product of Hilbert spaces
associated to regions with boundary. The latter Hilbert spaces include degrees
of freedom on the entangling surface that transform like surface charges under
the gauge symmetry. These degrees of freedom are shown to contribute to the
entanglement entropy, and the form of this contribution is determined by the
gauge symmetry. We test our definition using the example of two-dimensional
Yang-Mills theory, and find that it agrees with the thermal entropy in de
Sitter space, and with the results of the Euclidean replica trick. We discuss
the possible implications of this result for more complicated gauge theories,
including quantum gravity.
