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 \( \mathbb{C} \) 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 \( {\omega}_p^2={c}_{x y}^2\left({p}_x^2+{p}_y^2\right)+{c}_z^2{p}_z^2 \). 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.
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Kobayashi, M., Nakano, E. & Nitta, M. Color magnetism in non-Abelian vortex matter. J. High Energ. Phys. 2014, 130 (2014). https://doi.org/10.1007/JHEP06(2014)130
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DOI: https://doi.org/10.1007/JHEP06(2014)130