Entanglement in Weakly Coupled Lattice Gauge Theories

We present a direct lattice gauge theory computation that, without using dualities, demonstrates that the entanglement entropy of Yang-Mills theories with arbitrary gauge group $G$ contains a generic logarithmic term at sufficiently weak coupling $e$. In two spatial dimensions, for a region of linear size $r$, this term equals $\frac{1}{2} \dim(G) \log\left(e^2 r\right)$ and it dominates the universal part of the entanglement entropy. Such logarithmic terms arise from the entanglement of the softest mode in the entangling region with the environment. For Maxwell theory in two spatial dimensions, our results agree with those obtained by dualizing to a compact scalar with spontaneous symmetry breaking.