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Critical distance and Crofton form in confining geometries


For two symmetric strips with equal and finite size and in the background of several confining geometries, we numerically calculate the critical distance between these two mixed systems where the mutual information between them drops to zero and show that this quantity could be a useful correlation measure in probing the phase structures of holographic QCD models. The models that we consider here are Sakai–Sugimoto and deformed Sakai–Sugimoto, Klebanov–Tseytlin and Maldacena–Nunez. For evaluating the structures of these holographic supergravity geometries from the perspective of the bulk reconstruction, we also calculate their Crofton forms and show that there is a universal behavior in the confining backgrounds where a “well functionality” is present around the IR cut-off point, and far from the IR wall the scalar part of the Crofton form would become constant, demonstrating the effects of the wall of the confining models on the phase structures. This work is the shorter version of our previous work arXiv:2110.12970 (Ghodrati, Phys. Rev. D 104(4):046004, 2021) with few more results about the connections between phases.

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I would like to thank Tuna Demircik for useful discussions. This work has been supported by an appointment to the JRG Program at the APCTP through the Science and Technology Promotion Fund and Lottery Fund of the Korean Government. It has also been supported by the Korean Local Governments—Gyeongsangbuk-do Province and Pohang City—and by the National Research Foundation of Korea (NRF) funded by the Korean government (MSIT) (grant number 2021R1A2C1010834).

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Correspondence to Mahdis Ghodrati.

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Ghodrati, M. Critical distance and Crofton form in confining geometries. J. Korean Phys. Soc. 81, 77–90 (2022).

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  • Mixed states
  • Holography
  • Entanglement entropy
  • Confining geometries
  • Crofton form