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Pion condensation and pion star from holographic QCD

Yidian Chen1,*, Mingshan Ding1,†, Danning Li2,‡, Kazem Bitaghsir Fadafan3,§, and Mei Huang4,∥

  • *Contact author: chenyidian@hznu.edu.cn
  • †Contact author: 13149710203@163.com
  • ‡Contact author: lidanning@jnu.edu.cn
  • §Contact author: bitaghsir@shahroodut.ac.ir
  • ∥Contact author: huangmei@ucas.ac.cn
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Phys. Rev. D 111, 126010 – Published 17 June, 2025

DOI: https://doi.org/10.1103/94zt-q2dw

Abstract

The properties of quantum chromodynamics (QCD) matter at finite isospin densities are investigated employing holographic hard-wall and soft-wall anti–de Sitter (AdS)/QCD models. It is confirmed that at high enough isospin densities, charged pions start to condense and the pion superfluid phase appears in the system. It is shown that the chiral condensate and the pion condensate can be transformed to each other and form a chiral circle in the superfluid phase. We derived the equation of state (EoS) for pionic matter, calculated the normalized trace anomaly Δ and (ε−3p)/mπ4, and analyzed the sound speed and adiabatic index. Additionally, we provided data on the mass-radius relation and tidal deformability of pion stars. The results indicate that the holographic models align well with lattice QCD concerning isospin density, axial-vector condensation, EoS, and trace anomaly, though discrepancies in sound speed and adiabatic index emerge at higher isospin chemical potentials. The holographic models closely match the leading-order results from chiral perturbation theory (χPT) in certain observables, suggesting that they may effectively capture aspects of χPT dynamics within a five-dimensional framework under the probe approximation.

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Phys. Rev. D 111, 126010– Published 17 June, 2025
  • Received 10 September 2024
  • Accepted 28 May 2025
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