  The vacuum entanglement entropy of Maxwell theory, when evaluated by standard
methods, contains an unexpected term with no known statistical interpretation.
We resolve this two-decades old puzzle by showing that this term is the
entanglement entropy of edge modes: classical solutions determined by the
electric field normal to the entangling surface. We explain how the heat kernel
regularization applied to this term leads to the negative divergent expression
found by Kabat. This calculation also resolves a recent puzzle concerning the
logarithmic divergences of gauge fields in 3+1 dimensions.
