Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice
Abstract QCD matter in strong magnetic field exhibits a rich phase structure. In the presence of an external magnetic field, the chiral Lagrangian for two flavors is accompanied by the Wess-Zumino-Witten (WZW) term containing an anomalous coupling of the neutral pion π 0 to the magnetic field via th...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-12-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2023)032 |
| _version_ | 1797233860586504192 |
|---|---|
| author | Minoru Eto Kentaro Nishimura Muneto Nitta |
| author_facet | Minoru Eto Kentaro Nishimura Muneto Nitta |
| author_sort | Minoru Eto |
| collection | DOAJ |
| description | Abstract QCD matter in strong magnetic field exhibits a rich phase structure. In the presence of an external magnetic field, the chiral Lagrangian for two flavors is accompanied by the Wess-Zumino-Witten (WZW) term containing an anomalous coupling of the neutral pion π 0 to the magnetic field via the chiral anomaly. Due to this term, the ground state is inhomogeneous in the form of either chiral soliton lattice (CSL), an array of solitons in the direction of magnetic field, or domain-wall Skyrmion (DWSk) phase in which Skyrmions supported by π 3[SU(2)] ≃ ℤ appear inside the solitons as topological lumps supported by π 2(S 2) ≃ ℤ in the effective worldvolume theory of the soliton. In this paper, we determine the phase boundary between the CSL and DWSk phases beyond the single-soliton approximation, within the leading order of chiral perturbation theory. To this end, we explore a domain-wall Skyrmion chain in multiple soliton configurations. First, we construct the effective theory of the CSL by the moduli approximation, and obtain the ℂP 1 model or O(3) model, gauged by a background electromagnetic gauge field, with two kinds of topological terms coming from the WZW term: one is the topological lump charge in 2+1 dimensional worldvolume and the other is a topological term counting the soliton number. Topological lumps in the 2+1 dimensional worldvolume theory are superconducting rings and their sizes are constrained by the flux quantization condition. The negative energy condition of the lumps yields the phase boundary between the CSL and DWSk phases. We find that a large region inside the CSL is occupied by the DWSk phase, and that the CSL remains metastable in the DWSk phase in the vicinity of the phase boundary. |
| first_indexed | 2024-03-08T22:42:47Z |
| format | Article |
| id | doaj.art-e5ed198b502843cea19f81135138cc92 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-24T16:22:53Z |
| publishDate | 2023-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-e5ed198b502843cea19f81135138cc922024-03-31T11:08:46ZengSpringerOpenJournal of High Energy Physics1029-84792023-12-0120231212210.1007/JHEP12(2023)032Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton latticeMinoru Eto0Kentaro Nishimura1Muneto Nitta2Department of Physics, Yamagata UniversityResearch and Education Center for Natural Sciences, Keio UniversityResearch and Education Center for Natural Sciences, Keio UniversityAbstract QCD matter in strong magnetic field exhibits a rich phase structure. In the presence of an external magnetic field, the chiral Lagrangian for two flavors is accompanied by the Wess-Zumino-Witten (WZW) term containing an anomalous coupling of the neutral pion π 0 to the magnetic field via the chiral anomaly. Due to this term, the ground state is inhomogeneous in the form of either chiral soliton lattice (CSL), an array of solitons in the direction of magnetic field, or domain-wall Skyrmion (DWSk) phase in which Skyrmions supported by π 3[SU(2)] ≃ ℤ appear inside the solitons as topological lumps supported by π 2(S 2) ≃ ℤ in the effective worldvolume theory of the soliton. In this paper, we determine the phase boundary between the CSL and DWSk phases beyond the single-soliton approximation, within the leading order of chiral perturbation theory. To this end, we explore a domain-wall Skyrmion chain in multiple soliton configurations. First, we construct the effective theory of the CSL by the moduli approximation, and obtain the ℂP 1 model or O(3) model, gauged by a background electromagnetic gauge field, with two kinds of topological terms coming from the WZW term: one is the topological lump charge in 2+1 dimensional worldvolume and the other is a topological term counting the soliton number. Topological lumps in the 2+1 dimensional worldvolume theory are superconducting rings and their sizes are constrained by the flux quantization condition. The negative energy condition of the lumps yields the phase boundary between the CSL and DWSk phases. We find that a large region inside the CSL is occupied by the DWSk phase, and that the CSL remains metastable in the DWSk phase in the vicinity of the phase boundary.https://doi.org/10.1007/JHEP12(2023)032Phase Diagram or Equation of StateChiral LagrangianSolitons Monopoles and Instantons |
| spellingShingle | Minoru Eto Kentaro Nishimura Muneto Nitta Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice Journal of High Energy Physics Phase Diagram or Equation of State Chiral Lagrangian Solitons Monopoles and Instantons |
| title | Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice |
| title_full | Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice |
| title_fullStr | Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice |
| title_full_unstemmed | Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice |
| title_short | Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice |
| title_sort | phase diagram of qcd matter with magnetic field domain wall skyrmion chain in chiral soliton lattice |
| topic | Phase Diagram or Equation of State Chiral Lagrangian Solitons Monopoles and Instantons |
| url | https://doi.org/10.1007/JHEP12(2023)032 |
| work_keys_str_mv | AT minorueto phasediagramofqcdmatterwithmagneticfielddomainwallskyrmionchaininchiralsolitonlattice AT kentaronishimura phasediagramofqcdmatterwithmagneticfielddomainwallskyrmionchaininchiralsolitonlattice AT munetonitta phasediagramofqcdmatterwithmagneticfielddomainwallskyrmionchaininchiralsolitonlattice |