HEE and HSC for flavors: perturbative structure in open string geometries

Introduction of electric field in the D-brane worldvolume induces a horizon in the open string geometry perceived by the brane fluctuations. We study the holographic entanglement entropy (HEE) and subregion complexity (HSC) in these asymptotically AdS geometries in three, four and five dimensions aiming to capture these quantities in the flavor sector introduced by the D-branes. Both the strip and spherical subregions have been considered. We show that the Bekenstein-Hawking entropy associated with the open string horizon, which earlier failed to reproduce the thermal entropy in the boundary, now precisely matches with the entanglement entropy at high temperatures. We check the validity of embedding function theorem while computing the HEE and attempt to reproduce the first law of entanglement thermodynamics, at least at leading order. On the basis of obtained results, we also reflect upon consequences of applying Ryu-Takayanagi proposal on these non-Einstein geometries.