Abstract
In earlier work, we introduced a dynamical Einstein-Maxwell-dilaton model which mimics essential features of QCD (thermodynamics) below and above deconfinement. Although there are some subtle differences in the confining regime of our model as compared to the standard results, we do have a temperature dependent dual metric below Tc as well, allowing for a richer and more realistic holographic modeling of the QCD phase structure. We now discuss how these features leave their imprints on the associated entanglement entropy when a strip region is introduced in the various phases. We uncover an even so rich structure in the entanglement entropy, consistent with the thermodynamical transitions, while again uncloaking some subtleties. Thanks to the temperature dependent confining geometry, we can present an original quantitative prediction for the phase diagram in terms of temperature and strip length, reporting a critical end point at the deconfinement temperature. We also generalize to the case with chemical potential.
Highlights
On the other hand, QCD is the well-tested theory of sub-atomic particles carrying strongly interacting color charge, which at low temperatures and densities are bound together in colorless hadronic bound states due to confinement
In earlier work, we introduced a dynamical Einstein-Maxwell-dilaton model which mimics essential features of QCD below and above deconfinement
Constructing a gravity theory capable of describing properties of real QCD and from which testable predictions can be extracted is of importance, both to support or complement other takes on the same problem, coming from e.g. lattice QCD, Dyson-Schwinger or Functional Renormalization Group equations, effective QCD models, etc
Summary
Our aim in this subsection is to investigate the entanglement entropy in the above mentioned specious-confined/deconfined phases. Whereas in the confined phase the order of the entanglement entropy changes at certain length c, no such thing happens in the specious-confined phase This difference further underlines the subtle interpretation of the small black hole phase as being strictly dual to the confined phase Our main aim here is to investigate whether the entanglement entropy can capture the difference between the small/large black hole ( between the dual specious-confined/deconfined) phase transition as for the thermal-AdS/black hole (or the dual confined/deconfined) phase transition in the previous section. The entangling surface, which propagates in the bulk, again experiences the effects caused by the changing geometry of the black hole phase transitions These similarities again highlight the effectiveness of entanglement entropy to probe black hole and dual specious-confined/deconfined phase transition, yet again, without providing any information about the critical temperature.
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