Holographic confining-deconfining gauge theories and entanglement measures with a magnetic field

We study various holographic pure and mixed-state entanglement measures in the confined/deconfined phases of a bottom-up AdS/QCD model in the presence of a background magnetic field. We analyze the entanglement entropy, entanglement wedge cross section, mutual information, and entanglement negativity and investigate how a background magnetic field leaves its imprints on the entanglement structure of these measures. Due to the anisotropy introduced by the magnetic field, we find that the behavior of these measures depends nontrivially on the relative orientation of the strip with respect to the field. In the confining phase, the entanglement entropy and negativity undergo a phase transition at the same critical strip length, the magnitude of which increases/decreases for parallel/perpendicular orientation of the magnetic field. The entanglement wedge cross section similarly displays discontinuous behavior each time a phase transition between different entangling surfaces occurs, while further exhibiting anisotropic features with a magnetic field. We further find that the magnetic field also introduces substantial changes in the entanglement measures of the deconfined phase; however, these changes remain qualitatively similar for all orientations of the magnetic field. We further study the inequality involving the entanglement wedge and mutual information and find that the former always exceeds half of the latter everywhere in the parameter space of the confined/deconfined phases.