Journal of Holography Applications in Physics
Domain Wall Skyrmions in Holographic Quantum Chromodynamics: Topological Phases and Phase Transitions
Document Type : Regular article
Authors
1 OSTIM Technical University, Department of Computer Engineering, 06374 Ankara, Turkiye
2 Eastern Mediterranean University, Physics Department, Famagusta, 99628 North Cyprus, via Mersin 10, Turkiye
Abstract
We investigate the domain wall skyrmions phase in the framework of holographic quantum chromodynamics (QCD) using the Sakai-Sugimoto model. Building on previous work regarding chiral soliton lattices (CSLs) in strong magnetic fields, we study the emergence of localized skyrmions a top domain walls formed by CSLs. These skyrmions, realized as undissolved D4-branes embedded in the D8-branes, carry baryon number two and exhibit complex topological and energetic features. We explore the interplay between magnetic field strength, pion mass, and baryon chemical potential in stabilizing these configurations and demonstrate the existence of a mixed CSL-skyrmions phase. Through systematic energy analysis, we establish that the domain wall skyrmions become energetically favorable when $\mu_B |B| \gtrsim \Lambda \cdot m_\pi f_\pi^2$, with the transition occurring around $\mu_B |B| \sim 4.5$ in our holographic framework. Our phase diagram reveals three distinct regions: the CSL phase at low chemical potential and magnetic field, the domain wall skyrmions phase at intermediate scales, and a conjectured skyrmions crystal phase at the highest densities. The instanton density profiles $\text{Tr}(F \wedge F)$ show sharp localization in the domain wall skyrmions phase, contrasting with the smooth, extended distribution characteristic of the pure CSL configuration. These findings provide non-perturbative insights into baryonic matter in the dense QCD and offer a geometrical picture of topological phase transitions via string theory duality, with potential applications to neutron star physics and the broader QCD phase diagram under extreme conditions.
Keywords
- Domain wall Skyrmion
- holographic QCD
- Sakai-Sugimoto model
- chiral soliton lattices (CSLs)
- Topological Phases
- Phase Transitions
Main Subjects
Article PDF
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[44] D. T. Son and M. A. Stephanov, “QCD and dimensional deconstruction”, Phys. Rev. D 69, 065020 (2004) [arXiv:hep-ph/0304182]
[45] U. Gürsoy, M. Järvinen, G. Nijs and J. F. Pedraza, “On the interplay between magnetic field and anisotropy in holographic QCD”, JHEP 03, 180 (2021) [arXiv:2011.09474 [hepth]]
[46] T. Brauner and N. Yamamoto, “Chiral Soliton Lattice and Charged Pion Condensation in Strong Magnetic Fields”, JHEP 04, 132 (2017) [arXiv:1609.05213 [hep-ph]]
[47] K. Hashimoto, T. Sakai and S. Sugimoto, “Holographic baryons: Static properties and form factors from gauge/string duality”, Prog. Theor. Phys. 120, 1093 (2008) [arXiv:0806.3122 [hep-th]]
[48] D. K. Hong, M. Rho, H. U. Yee and P. Yi, “Chiral dynamics of baryons from string theory”, Phys. Rev. D 76, 061901 (2007) [arXiv:hep-th/0701276]
[49] A. Pomarol and A. Wulzer, “Baryon physics in holographic QCD”, Nucl. Phys. B 809, 347 (2009) [arXiv:0807.0316 [hep-ph]]
[50] O. Aharony, J. Sonnenschein and S. Yankielowicz, “A holographic model of deconfinement and chiral symmetry restoration”, Ann. Phys. 322, 1420 (2007) [arXiv:hepth/0604161]
[51] A. Karch, A. O’Bannon and K. Skenderis, “Holographic renormalization of probe Dbranes in AdS/CFT”, JHEP 04, 015 (2006) [arXiv:hep-th/0512125]
[52] C. Hoyos-Badajoz, K. Landsteiner and S. Montero, “Holographic meson melting”, JHEP 04, 031 (2007) [arXiv:hep-th/0612169]
[53] J. Park and P. Yi, “A holographic QCD and excited baryons from string theory”, JHEP 06, 011 (2008) [arXiv:0804.2926 [hep-th]]
[54] T. Brauner and N. Yamamoto, “Chiral Soliton Lattice and Charged Pion Condensation in Strong Magnetic Fields”, JHEP 04, 132 (2017) [arXiv:1609.05213 [hep-ph]]
[55] Z. Li, D. Li and M. Huang, “Jet quenching and quark energy loss from holographic QCD”, Phys. Rev. D 111(12), 126019 (2025) [arXiv:2504.04147 [hep-ph]]
[56] N. Evans, A. Gebauer, K. Y. Kim and M. Magou, “Holographic description of the phase diagram of a chiral symmetry breaking gauge theory”, JHEP 03, 132 (2010) [arXiv:1002.1885 [hep-th]]
[57] F. Preis, A. Rebhan and A. Schmitt, “Holographic baryonic matter in a background magnetic field”, J. Phys. G 39, 054006 (2012) [arXiv:1109.6904 [hep-th]]
[58] V. G. Filev, C. V. Johnson, R. C. Rashkov and K. S. Viswanathan, “Flavoured large N gauge theory in an external magnetic field”, JHEP 10, 019 (2007) [arXiv:hepth/0701001]
[59] M. Berenguer, J. Mas, M. Matsumoto, K. Murata and A. V. Ramallo, “Chiral symmetry breaking and restoration by helical magnetic fields in AdS/CFT”, JHEP 05, 048 (2025) [arXiv:2502.19197 [hep-th]]
[60] D. E. Kharzeev, L. D. McLerran and H. J. Warringa, “The Effects of topological charge change in heavy ion collisions: ’Event by event P and CP violation”’, Nucl. Phys. A 803, 227 (2008) [arXiv:0711.0950 [hep-ph]]
[61] T. Brauner and N. Yamamoto, “Chiral Soliton Lattice and Charged Pion Condensation in Strong Magnetic Fields”, JHEP 04, 132 (2017) [arXiv:1609.05213 [hep-ph]]
[62] M. Eto, Y. Isozumi, M. Nitta, K. Ohashi, K. Ohta and N. Sakai, “D-brane construction for non-Abelian walls”, Phys. Rev. D 71, 125006 (2005) [arXiv:hep-th/0412024]
[63] Y. Hidaka, K. Kamikado, T. Kanazawa and T. Noumi, “Phonons, pions and quasilong-range order in spatially modulated chiral condensates”, Phys. Rev. D 92, 034003 (2015) [arXiv:1505.00848 [hep-ph]]
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Volume 5, Issue 3
September 2025Pages 12-30
- Receive Date: 30 June 2025
- Revise Date: 09 August 2025
- Accept Date: 09 August 2025