Testing bare open-string-metric areas against flavour entanglement in finite-density D3-D7
We test whether bare codimension-two areas in the D7-brane open string metric (OSM) reproduce the leading probe-brane contribution to boundary entanglement entropy in the massless finite-density D3-D7 system at zero temperature. The established Chang-Karch-Uhlemann benchmark contains shape-dependent volume terms in a controlled probe regime. By contrast, the connected strip family terminates at a maximal width and the selected strip finite part saturates at the disconnected-reference value, while the lower-area spherical branch is area-like rather than volume-like at large radius. The OSM construction nevertheless detects the density-induced crossover scale, and its geometric landmarks occur at order-one multiples of a pole-defined longitudinal response length. A low-temperature regulator shows that no density-controlled horizon-volume term survives the zero-temperature limit. Bare OSM areas therefore diagnose open-sector crossover physics but do not, in general, compute flavour entanglement entropy.