Entanglement entropy of electromagnetic edge modes

TL;DR

The paper demonstrates that the puzzling contact term in gauge-field entanglement entropy is the statistical entropy of edge modes—electric flux on the entangling surface—by employing a brick-wall regulator and edge-mode sums. It shows that including edge modes reconciles the geometric (Euclidean) entropy with the von Neumann entropy and fixes universal logarithmic terms to match the conformal anomaly in 3+1 dimensions. The results provide a concrete, regulator-dependent mechanism linking edge degrees of freedom to Kabat’s contact term and have implications for black hole entropy, lattice vs continuum regularizations, and potential extensions to nonabelian gauge theories and gravity.

Abstract

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.