On the Entanglement Entropy of Maxwell Theory: A Condensed Matter Perspective

Understand

Despite the seeming simplicity of the theory, calculating (and even defining) entanglement entropy for the Maxwell theory of a $U(1)$ gauge field in (3+1) dimensions has been the subject of controversy.

• It is generally accepted that the ground state entanglement entropy for a region of linear size $L$ behaves as an area law with a subleading logarithm, $S = \alpha L^2 -\gamma \log L$.
• While the logarithmic coefficient $\gamma$ is believed to be universal, there has been disagreement about its precise value.
• After carefully accounting for subtle boundary corrections, multiple analyses in the high energy literature have converged on an answer related to the conformal trace anomaly, which is only sensitive to the local curvature of the partition.