Color Magnetism in Non-Abelian Vortex Matter

Abstract

We propose color magnetism as a generalization of the ordinary Heisenberg (anti-)ferro magnets on a triangular lattice. Vortex matter consisting of an Abrikosov lattice of non-Abelian vortices with color magnetic fluxes shows a color ferro or anti-ferro magnetism, depending on the interaction among the vortex sites. A prime example is a non-Abelian vortex lattice in rotating dense quark matter, showing a color ferromagnetism. We show that the low-energy effective theory for the vortex lattice system in the color ferromagnetic phase is described by a 3+1 dimensional $C{P}^{N-1}$ nonlinear sigma model with spatially anisotropic couplings. We identify gapless excitations independent from Tkachenko modes as color magnons, that is, Nambu-Goldstone modes propagating in the vortex lattice with an anisotropic linear dispersion relation ${\omega }_p^2=c_{xy}^2(p_x^2+p_y^2)+c_z^2{p}_z^2$. We calculate the transition temperature between the ordered and disordered phases, and apply it to dense quark matter. We also identify the order parameter spaces for color anti-ferromagnets.

7 pages, no figures, published version

References in corpus (10)

• Color superconductivity in dense quark matter
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Magnetic Fields Boosted by Gluon Vortices in Color Superconductivity
• Chromomagnetic Instability and Induced Magnetic Field in Neutral Two-Flavor Color Superconductivity
• Signature of a Z_2 vortex in the dynamical correlations of the triangular-lattice Heisenberg antiferromagnet
• Confined Monopoles Induced by Quantum Effects in Dense QCD
• Confined Magnetic Monopoles in Dense QCD
• Topological Interactions of Non-Abelian Vortices with Quasi-Particles in High Density QCD
• Static Interactions of non-Abelian Vortices
• Anisotropic Optical Response of Dense Quark Matter under Rotation: Compact Stars as Cosmic Polarizers

Cited by in corpus (19)

• Short range inter-vortex interaction and interacting dynamics of half-quantized vortices in two-component Bose-Einstein condensates
• Non-Abelian strings and domain walls in two Higgs doublet models
• Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and $\mathbb{C}{P}^{N-1}$ Lumps
• Quark-hadron continuity under rotation: Vortex continuity or boojum?
• Phases of rotating baryonic matter: non-Abelian chiral soliton lattices, antiferro-isospin chains, and ferri/ferromagnetic magnetization
• Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice
• $\mathbb{C}{P}^2$ Skyrmion Crystals in an SU(3) Magnet with a Generalized Dzyaloshinskii-Moriya Interaction
• Aharonov-Bohm Phase in High Density Quark Matter
• Multi-Skyrmions with orientational moduli
• Topological Defects in the Georgi-Machacek Model
• Coupling between Majorana fermions and Nambu-Goldstone bosons inside a non-Abelian vortex in dense QCD
• $SU(3)$ Knot Solitons: Hopfions in the $F_2$ Skyrme-Faddeev-Niemi model
• Chiral non-Abelian vortices and their confinement in three flavor dense QCD
• BPS Sphalerons in the $F_2$ Non-Linear Sigma Model
• Low-energy Effective Worldsheet theory of a non-Abelian vortex in high-density QCD Revisited: A regular gauge construction
• Non-Abelian vortex lattices
• Dyonic non-Abelian vortex strings in supersymmetric and non-supersymmetric theories: tensions and higher derivative corrections
• Stable non-Abelian semi-superfluid vortices in dense QCD
• Chiral non-Abelian vortex molecules in dense QCD