{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T01:03:45Z","timestamp":1775523825710,"version":"3.50.1"},"reference-count":88,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T00:00:00Z","timestamp":1739145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Kaon condensation in hyperon-mixed matter [(Y+K) phase], which may be realized in neutron stars, is discussed on the basis of chiral symmetry. With the use of the effective chiral Lagrangian for kaon\u2013baryon and kaon\u2013kaon interactions; coupled with the relativistic mean field theory and universal three-baryon repulsive interaction, we clarify the effects of the s-wave kaon\u2013baryon scalar interaction simulated by the kaon\u2013baryon sigma terms and vector interaction (Tomozawa\u2013Weinberg term) on kaon properties in hyperon-mixed matter, the onset density of kaon condensation, and the equation of state with the (Y+K) phase. In particular, the quark condensates in the (Y+K) phase are obtained, and their relevance to chiral symmetry restoration is discussed.<\/jats:p>","DOI":"10.3390\/sym17020270","type":"journal-article","created":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T06:43:07Z","timestamp":1739169787000},"page":"270","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Chiral Symmetry in Dense Matter with Meson Condensation"],"prefix":"10.3390","volume":"17","author":[{"given":"Takumi","family":"Muto","sequence":"first","affiliation":[{"name":"Department of Physics, Chiba Institute of Technology, Chiba 275-0023, Japan"}]},{"given":"Toshiki","family":"Maruyama","sequence":"additional","affiliation":[{"name":"Advanced Science Research Center, Japan Atomic Energy Agency, Ibaraki 319-1195, Japan"}]},{"given":"Toshitaka","family":"Tatsumi","sequence":"additional","affiliation":[{"name":"52-4 Kitashirakawa Kamiikeda-Cho, Kyoto 606-8287, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1103\/PhysRevLett.29.382","article-title":"Condensed \u03c0\u2212 phase in neutron-star matter","volume":"29","author":"Sawyer","year":"1972","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1103\/PhysRevLett.29.386","article-title":"\u03c0\u2212 condensate in dense nuclear matter","volume":"29","author":"Scalapino","year":"1972","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1103\/RevModPhys.50.107","article-title":"Pion fields in nuclear matter","volume":"50","author":"Migdal","year":"1978","journal-title":"Rev. Mod. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/0370-1573(90)90132-L","article-title":"Pion degrees of freedom in nuclear matter","volume":"192","author":"Migdal","year":"1990","journal-title":"Phys. Rep."},{"key":"ref_5","unstructured":"Rho, M., and Wilkinson, D.H. (1979). Mesons and Nuclei, North Holland."},{"key":"ref_6","first-page":"1","article-title":"Various phases in high-density nuclear matter and neutron stars","volume":"112","author":"Kunihiro","year":"1993","journal-title":"Prog. Theor. Phys. Suppl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/0370-2693(86)90331-X","article-title":"Strange goings on in dense nucleonic matter","volume":"175","author":"Kaplan","year":"1986","journal-title":"Phys. Lett. B"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1143\/PTP.80.22","article-title":"K-on condensation and cooling of neutron stars","volume":"80","author":"Tatsumi","year":"1988","journal-title":"Prog. Theor. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0370-2693(92)90001-K","article-title":"Theoretical aspects of kaon condensation in neutron matter","volume":"283","author":"Muto","year":"1992","journal-title":"Phys. Lett. B"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1143\/ptp\/89.2.415","article-title":"Role of weak interaction on kaon condensation in neutron matter\u2013A result with hyperon excitations","volume":"89","author":"Muto","year":"1993","journal-title":"Prog. Theor. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1143\/PTPS.112.159","article-title":"A chiral symmetry approach to meson condensations","volume":"112","author":"Muto","year":"1993","journal-title":"Prog. Theor. Phys. Suppl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1143\/PTPS.112.221","article-title":"Implications of various hadron phases to neutron star phenomena","volume":"112","author":"Muto","year":"1993","journal-title":"Prog. Theor. Phys. Suppl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1016\/0375-9474(94)90407-3","article-title":"Composition, structure and evolution of neutron stars with kaon condensates","volume":"572","author":"Thorsson","year":"1994","journal-title":"Nucl. Phys. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1016\/0375-9474(95)00084-E","article-title":"Kaon polarization in nuclear matter","volume":"588","author":"Kolomeitsev","year":"1995","journal-title":"Nucl. Phys. A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/0375-9474(94)00623-U","article-title":"An Effective chiral Lagrangian approach to kaon - nuclear interactions: Kaonic atom and kaon condensation","volume":"585","author":"Lee","year":"1995","journal-title":"Nucl. Phys. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/0370-1573(96)00005-1","article-title":"Kaon condensation in dense stellar matter","volume":"275","author":"Lee","year":"1996","journal-title":"Phys. Rep."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0370-1573(96)00023-3","article-title":"Composition and Structure of Protoneutron Stars","volume":"280","author":"Prakash","year":"1997","journal-title":"Phys. Rep."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/S0370-2693(98)00488-2","article-title":"In-medium kaon and antikaon properties in the quark-meson coupling model","volume":"429","author":"Tsushima","year":"1998","journal-title":"Phys. Lett. B"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1016\/0375-9474(95)00451-3","article-title":"Equation of state with kaon condensates and neutron stars","volume":"597","author":"Fujii","year":"1996","journal-title":"Nucl. Phys. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"025803","DOI":"10.1103\/PhysRevC.60.025803","article-title":"First order kaon condensate","volume":"60","author":"Glendenning","year":"1999","journal-title":"Phys. Rev. C"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1086\/155447","article-title":"Beta decay of pion condensates as a cooling mechanism for neutron stars","volume":"216","author":"Maxwell","year":"1977","journal-title":"Astrophys. J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2042","DOI":"10.1103\/PhysRevD.37.2042","article-title":"Strangeness condensation and cooling of neutron stars","volume":"37","author":"Brown","year":"1988","journal-title":"Phys. Rev. D"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1016\/0375-9474(94)90719-6","article-title":"Effects of weak interaction on kaon condensation and cooling of neutron stars","volume":"571","author":"Fujii","year":"1994","journal-title":"Nucl. Phys. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3140","DOI":"10.1103\/PhysRevC.50.3140","article-title":"Effects of symmetry energy on the direct URCA process in the kaon condensed phase","volume":"50","author":"Fujii","year":"1994","journal-title":"Phys. Rev. C"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/0370-2693(95)00231-9","article-title":"Kaon condensation in neutron star matter with hyperons","volume":"349","author":"Ellis","year":"1995","journal-title":"Phys. Lett. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3470","DOI":"10.1103\/PhysRevC.52.3470","article-title":"Strangeness in hadronic stellar matter","volume":"52","author":"Knorren","year":"1995","journal-title":"Phys. Rev. C"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1416","DOI":"10.1103\/PhysRevC.53.1416","article-title":"Hyperon-rich matter in neutron stars","volume":"53","author":"Schaffner","year":"1996","journal-title":"Phys. Rev. C"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1016\/S0375-9474(00)00175-5","article-title":"Antikaon condensation in neutron stars","volume":"674","author":"Pal","year":"2000","journal-title":"Nucl. Phys. A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"015810","DOI":"10.1103\/PhysRevC.77.015810","article-title":"Interplay between kaon condensation and hyperons in highly dense matter","volume":"77","author":"Muto","year":"2008","journal-title":"Phys. Rev. C"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1140\/epja\/i2010-10986-x","article-title":"Kaon properties in (proto-)neutron star matter","volume":"45","author":"Mishra","year":"2010","journal-title":"Eur. Phys. J. A"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"015801","DOI":"10.1103\/PhysRevC.90.015801","article-title":"Massive neutron stars with antikaon condensates in a density-dependent hadron field theory","volume":"90","author":"Char","year":"2014","journal-title":"Phys. Rev. C"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"96","DOI":"10.3847\/1538-4357\/abe860","article-title":"Equation-of-state Table with Hyperon and Antikaon for Supernova and Neutron Star Merger","volume":"910","author":"Malik","year":"2021","journal-title":"Astrophys. J."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"045804","DOI":"10.1103\/PhysRevC.107.045804","article-title":"Kaon-meson condensation and \u0394 resonance in hyperonic stellar matter within a relativistic mean-field model","volume":"107","author":"Ma","year":"2023","journal-title":"Phys. Rev. C"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"136587","DOI":"10.1016\/j.physletb.2021.136587","article-title":"Effects of three-baryon forces on kaon condensation in hyperon-mixed matter","volume":"820","author":"Muto","year":"2021","journal-title":"Phys. Lett. B"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Muto, T., Maruyama, T., and Tatsumi, T. (2022). Kaon-baryon coupling schemes and kaon condensation in hyperon-mixed matter. Prog. Theor. Exp. Phys., 2022.","DOI":"10.1093\/ptep\/ptac115"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Muto, T. (2024). Properties of kaon-condensed phase in hyperon-mixed matter with three-baryon forces. arXiv.","DOI":"10.1103\/PhysRevC.111.045802"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/S0375-9474(01)01226-X","article-title":"Kaonic modes in hyperonic matter and p-wave kaon condensation","volume":"697","author":"Muto","year":"2002","journal-title":"Nucl. Phys. A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"083C01","DOI":"10.1093\/ptep\/ptaa104","article-title":"Review of Particle Physics","volume":"2020","author":"Zyla","year":"2020","journal-title":"Prog. Theor. Exp. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1881","DOI":"10.1103\/PhysRevC.45.1881","article-title":"Quark and gluon condensates in nuclear matter","volume":"45","author":"Cohen","year":"1992","journal-title":"Phys. Rev. C"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1143\/PTP.119.965","article-title":"Universal short-range repulsion in the baryon system originating from the confinement: Approach in string-junction model","volume":"119","author":"Tamagaki","year":"2008","journal-title":"Prog. Theor. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1063\/1.2932290","article-title":"Universal three-body repulsion suggested by neutron stars","volume":"1011","author":"Takatsuka","year":"2008","journal-title":"AIP Conf. Proc."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1143\/ptp\/92.1.93","article-title":"Properties of hot asymmetric nuclear matter","volume":"92","author":"Nishizaki","year":"1994","journal-title":"Prog. Theor. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/0375-9474(81)90241-4","article-title":"Variational calculations of realistic models of nuclear matter","volume":"359","author":"Lagaris","year":"1981","journal-title":"Nucl. Phys. A"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"015007","DOI":"10.1103\/RevModPhys.89.015007","article-title":"Equations of state for supernovae and compact stars","volume":"89","author":"Oertel","year":"2017","journal-title":"Rev. Mod. Phys."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1006\/aphy.1994.1090","article-title":"Multiply strange nuclear systems","volume":"235","author":"Schaffner","year":"1994","journal-title":"Ann. Phys."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"054502","DOI":"10.1103\/PhysRevD.78.054502","article-title":"Nucleon sigma term and strange quark content from lattice QCD with exact chiral symmetry","volume":"78","author":"Ohki","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"172001","DOI":"10.1103\/PhysRevLett.116.172001","article-title":"Lattice computation of the nucleon scalar quark contents at the physical point","volume":"116","author":"Durr","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"054517","DOI":"10.1103\/PhysRevD.102.054517","article-title":"Nucleon axial, tensor, and scalar charges and \u03c3-terms in lattice QCD","volume":"102","author":"Alexandrou","year":"2020","journal-title":"Phys. Rev. D"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/0370-2693(91)91394-B","article-title":"Sigma-term update","volume":"253","author":"Gasser","year":"1991","journal-title":"Phys. Lett. B"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1609","DOI":"10.1140\/epjs\/s11734-021-00145-6","article-title":"Brief history of the pion\u2013nucleon sigma term","volume":"230","year":"2021","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_51","first-page":"163","article-title":"The pattern of chiral symmetry breaking and the strange quark content of the proton","volume":"17","author":"Jaffe","year":"1987","journal-title":"Comm. Nucl. Part. Phys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/BF01579559","article-title":"Flavor mixing in the low energy hadron dynamics: Interplay of the SUf(3) breaking and the UA(1) anomaly","volume":"51","author":"Hatsuda","year":"1991","journal-title":"Z. Phys. C"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/S0375-9474(99)00846-5","article-title":"The properties of K\u00af in the nuclear medium","volume":"671","author":"Ramos","year":"2000","journal-title":"Nucl. Phys. A"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/S0375-9474(97)00020-1","article-title":"Effective kaon mass in dense baryonic matter: Role of correlations","volume":"617","author":"Waas","year":"1997","journal-title":"Nucl. Phys. A"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/S0375-9474(97)00487-9","article-title":"S-wave interactions of K\u00af and \u03b7 mesons in nuclear matter","volume":"625","author":"Waas","year":"1997","journal-title":"Nucl. Phys. A"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"123D01","DOI":"10.1093\/ptep\/ptaa139","article-title":"An event excess observed in the deeply bound region of the 12C (K\u2212, p) missing-mass spectrum","volume":"2020","author":"Ichikawa","year":"2020","journal-title":"Prog. Theor. Exp. Phys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"074503","DOI":"10.1103\/PhysRevD.87.074503","article-title":"Sigma terms from an SU(3) chiral extrapolation","volume":"87","author":"Shanahan","year":"2013","journal-title":"Phys. Rev. D"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"054505","DOI":"10.1103\/PhysRevD.90.054505","article-title":"Finite volume effects in the chiral extrapolation of baryon masses","volume":"90","author":"Lutz","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"063001","DOI":"10.1103\/PhysRevD.61.063001","article-title":"Nonequilibrium weak processes in kaon condensation. I. Reaction rate for the thermal kaon process","volume":"61","author":"Muto","year":"2000","journal-title":"Phys. Rev. D"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"083002","DOI":"10.1103\/PhysRevD.61.083002","article-title":"Nonequilibrium weak processes in kaon condensation. II. Kinetics of condensation","volume":"61","author":"Muto","year":"2000","journal-title":"Phys. Rev. D"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1086\/151216","article-title":"The ground state of matter at high densities: Equation of state and stellar models","volume":"170","author":"Baym","year":"1971","journal-title":"Astrophys. J."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1038\/nature09466","article-title":"A two-solar-mass neutron star measured using Shapiro delay","volume":"467","author":"Demorest","year":"2010","journal-title":"Nature"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"167","DOI":"10.3847\/0004-637X\/832\/2\/167","article-title":"The nanograv nine-year data set: Mass and geometric measurements of binary millisecond pulsars","volume":"832","author":"Fonseca","year":"2016","journal-title":"Astrophys. J."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1126\/science.1233232","article-title":"A massive pulsar in a compact relativistic binary","volume":"340","author":"Antoniadis","year":"2013","journal-title":"Science"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1038\/s41550-019-0880-2","article-title":"Relativistic Shapiro delay measurements of an extremely massive millisecond pulsar","volume":"4","author":"Cromartie","year":"2020","journal-title":"Nat. Astron."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"L12","DOI":"10.3847\/2041-8213\/ac03b8","article-title":"Refined mass and geometric measurements of the high-mass PSR J0740+6620","volume":"915","author":"Fonseca","year":"2021","journal-title":"Astrophys. J. L."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"L28","DOI":"10.3847\/2041-8213\/ac089b","article-title":"The radius of PSR J0740+6620 from NICER and XMM-Newton data","volume":"918","author":"Miller","year":"2021","journal-title":"Astrophys. J. L."},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Riley, T.E., Watts, A.L., Ray, P.S., Bogdanov, S., Guillot, S., Morsink, S.M., Bilous, A.V., Arzoumanian, Z., Choudhury, D., and Deneva, J.S. (2021). A NICER view of the massive pulsar PSR J0740+6620 informed by radio timing and XMM-Newton spectroscopy. Astrophys. J. L., 918.","DOI":"10.3847\/2041-8213\/ac0a81"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"L21","DOI":"10.3847\/2041-8213\/ab481c","article-title":"A NICER view of PSR J0030+0451: Millisecond pulsar parameter estimation","volume":"887","author":"Riley","year":"2019","journal-title":"Astrophys. J. L."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"L24","DOI":"10.3847\/2041-8213\/ab50c5","article-title":"PSR J0030+0451 mass and radius from NICER data and implications for the properties of neutron star matter","volume":"887","author":"Miller","year":"2019","journal-title":"Astrophys. J. L."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"1592","DOI":"10.1126\/science.1078070","article-title":"Determination of the equation of state of dense matter","volume":"298","author":"Danielewicz","year":"2002","journal-title":"Science"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"411","DOI":"10.3390\/particles2030025","article-title":"Meson Condensation","volume":"2019","author":"Mannarelli","year":"2019","journal-title":"Particles"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"034032","DOI":"10.1103\/PhysRevD.79.034032","article-title":"Fate of pion condensation in quark matter: From the chiral limit to the physical pion mass","volume":"79","author":"Abuki","year":"2009","journal-title":"Phys. Rev. D"},{"key":"ref_74","doi-asserted-by":"crossref","unstructured":"Khunjua, T.G., Klimenko, K.G., and Zhokhov, R.N. (2019). Charged pion condensation in dense quark matter: Nambu\u2013Jona-Lasinio model study. Symmetry, 2019.","DOI":"10.1007\/JHEP06(2019)006"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1140\/epjc\/s10052-020-08502-w","article-title":"Electrical neutrality and \u03b2-equilibrium conditions in dense quark matter: Generation of charged pion condensation by chiral imbalance","volume":"80","author":"Khunjua","year":"2020","journal-title":"Eur. Phys. J. C"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.1140\/epjc\/s10052-020-08574-8","article-title":"Quark and pion condensates at finite isospin density in chiral perturbation theory","volume":"80","author":"Adhikari","year":"2020","journal-title":"Eur. Phys. J. C"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1007\/JHEP06(2020)170","article-title":"Pion and kaon condensation at zero temperature in three-flavor \u03c7PPT at nonzero isospin and strange chemical potentials at next-to-leading order","volume":"06","author":"Adhikari","year":"2020","journal-title":"JHEP"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"045008","DOI":"10.1103\/PhysRevD.83.045008","article-title":"Ginzburg-Landau phase diagram for dense matter with axial anomaly, strange quark mass, and meson condensation","volume":"83","author":"Schmitt","year":"2011","journal-title":"Phys. Rev. D"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1088\/0004-637X\/764\/1\/12","article-title":"Hadron-quark crossover and massive hybrid stars with strangeness","volume":"764","author":"Masuda","year":"2013","journal-title":"Astrophys. J."},{"key":"ref_80","first-page":"021D01","article-title":"Hadron\u2013quark crossover and hot neutron stars at birth","volume":"2016","author":"Masuda","year":"2016","journal-title":"PTEP"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"42","DOI":"10.3847\/1538-4357\/ab441e","article-title":"New neutron star equation of state with quark\u2013hadron crossover","volume":"885","author":"Baym","year":"2019","journal-title":"Astrophys. J."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"074005","DOI":"10.1103\/PhysRevD.104.074005","article-title":"Stiffening of matter in quark-hadron continuity","volume":"104","author":"Kojo","year":"2021","journal-title":"Phys. Rev. D"},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"252702","DOI":"10.1103\/PhysRevLett.129.252702","article-title":"Trace anomaly as signature of conformality in neutron stars","volume":"129","author":"Fujimoto","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"ref_84","unstructured":"Tatsumi, T., and Nakano, E. (2004). Dual chiral density wave in quark matter. arXiv."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"114006","DOI":"10.1103\/PhysRevD.71.114006","article-title":"Chiral symmetry and density waves in quark matter","volume":"71","author":"Nakano","year":"2005","journal-title":"Phys. Rev. D"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"07402","DOI":"10.1103\/PhysRevD.61.074012","article-title":"Inverse meson mass ordering in the color-flavor-locking phase of high-density QCD","volume":"61","author":"Son","year":"2000","journal-title":"Phys. Rev. D"},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1016\/S0375-9474(01)01272-6","article-title":"High-density quark matter under stress","volume":"697","author":"Bedaque","year":"2002","journal-title":"Nucl. Phys. A"},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"054042","DOI":"10.1103\/PhysRevD.65.054042","article-title":"Novel phases and transitions in color flavor locked matter","volume":"65","author":"Kaplan","year":"2002","journal-title":"Phys. Rev. D"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/270\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T17:20:08Z","timestamp":1773854408000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/270"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,10]]},"references-count":88,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["sym17020270"],"URL":"https:\/\/doi.org\/10.3390\/sym17020270","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,10]]}}}