  We consider entanglement entropy between regions of space in lattice gauge
theory. The Hilbert space corresponding to a region of space includes edge
states that transform nontrivially under gauge transformations. By decomposing
the edge states in irreducible representations of the gauge group, the entropy
of an arbitrary state is expressed as the sum of three positive terms: a term
associated with the classical Shannon entropy of the distribution of boundary
representations, a term that appears only for non-Abelian gauge theories and
depends on the dimension of the boundary representations, and a term
representing nonlocal correlations. The first two terms are the entropy of the
edge states, and depend only on observables measurable at the boundary. These
results are applied to several examples of lattice gauge theory states,
including the ground state in the strong coupling expansion of Kogut and
Susskind. In all these examples we find that the entropy of the edge states is
the dominant contribution to the entanglement entropy.
