A note on entanglement entropy and topological defects in symmetric orbifold CFTs

In this brief note we calculate the entanglement entropy in $M^{\otimes N}\mathrm{/}{S}_N$ symmetric orbifold CFTs in the presence of topological defects, which were recently constructed in \cite{Gutperle:2024vyp,Knighton:2024noc}. We consider both universal defects which realize $Rep(S_N)$ non-invertible symmetry and non-universal defects. We calculate the sub-leading defect entropy/g-factor for defects at the boundary entangling surface as well as inside it.