Minoru Eto

Vortices and Other Topological Solitons in Dense Quark Matter

In this review, we discuss various properties of topological solitons in dense QCD matter, with a particular emphasis on the CFL phase exhibiting superfluidity and superconductivity, and their phenomenological implications in terms of the effective field theories such as the Ginzburg-Landau theory, the chiral Lagrangian, or the Bogoliubov--de Gennes equation. The most fundamental topological excitations are non-Abelian vortices, which are 1/3 quantized superfluid vortices and color magnetic flux tubes. They are created at a phase transition or a rotation such compact stars. The intervortex-interaction is repulsive and consequently a vortex lattice is formed. Bosonic and fermionic zero-energy modes are trapped in the vortex core and propagate along it as gapless excitations. The former consists of translational zero modes (a Kelvin mode) with a quadratic dispersion and CP(2) Nambu-Goldstone gapless modes with a linear dispersion, while the latter is the triplet Majorana fermion zero modes. The low-energy effective theory of the bosonic zero modes is a non-relativistic free complex scalar field and a CP(2) model in 1+1 dimensions. The effects of strange quark mass, electromagnetic interactions and non-perturbative quantum corrections are taken into account. Colorful boojums at the CFL interface, quantum color magnetic monopole confined by vortices, which supports the notion of quark-hadron duality, and Yang-Mills instantons inside a vortex as lumps are discussed. The interactions between a vortex and quasi-particles such as phonons, gluons, mesons, and photons are studied. A vortex lattice is shown to behave as a cosmic polarizer. Non-Abelian vortices are shown to behave as a novel kind of non-Abelian anyons. For the chiral symmetry breaking, we discuss fractional and integer axial domain walls, Abelian and non-Abelian axial vortices, axial wall-vortex composites, and Skyrmions.

Color Magnetic Flux Tubes in Dense QCD

QCD is expected to be in the color-flavor locking phase in high baryon density, which exhibits color superconductivity. The most fundamental topological objects in the color superconductor are non-Abelian vortices which are topologically stable color magnetic flux tubes. We present numerical solutions of the color magnetic flux tube for diverse choices of the coupling constants based on the Ginzburg-Landau Lagrangian. We also analytically study its asymptotic profiles and find that they are different from the case of usual superconductors. We propose the width of color magnetic fluxes and find that it is larger than naive expectation of the Compton wavelength of the massive gluon when the gluon mass is larger than the scalar mass.

Effective world-sheet theory of color magnetic flux tubes in dense QCD

Color magnetic flux tubes appear in the color-flavor locked phase of high density QCD, which exhibits color superconductivity as well as superfluidity. They are non-Abelian superfluid vortices and are accompanied by orientational zero modes in the internal space associated with the color-flavor locked symmetry spontaneously broken in the presence of the vortex. We show that those zero modes are localized around the vortex in spite of the logarithmic divergence of its tension, and derive the low-energy effective theory of them on the world-sheet of the vortex-string. e-mail addresses: meto(at)riken.jp; e.nakano(at)gsi.de; nitta(at)phys-h.keio.ac.jp.

Instabilities of Non-Abelian Vortices in Dense QCD

We construct a low-energy effective theory describing non-abelian vortices in the color superconducting quark matter under stress. We demonstrate that all the vortices are radically unstable against decay into the only one type of vortices due to the potential term induced by the explicit flavor symmetry breaking by the strange quark mass. A simple analytical estimate for the lifetime of unstable vortices is provided under the controlled weak-coupling calculations. We briefly discuss the (non)existence of magnetic monopoles at high density.

Higher Derivative Corrections to Non-Abelian Vortex Effective Theory

We give a systematic method to calculate higher derivative corrections to low-energy effective theories of solitons, which are in general nonlinear sigma models on the moduli spaces of the solitons. By applying it to the effective theory of a single BPS non-Abelian vortex in U(N) gauge theory with N fundamental Higgs fields, we obtain four derivative corrections to the effective sigma model on the moduli space C×CP N−1 . We compare them with the Nambu-Goto action and the Faddeev-Skyrme model. We also show that YangMills instantons/monopoles trapped inside a non-Abelian vortex membrane/string are not modified in the presence of higher derivative terms.

Interaction of half-quantized vortices in two-component Bose-Einstein condensates

We study the asymptotic interaction between two half-quantized vortices in two-component Bose-Einstein condensates. When two vortices in different components are placed at distance 2R, the leading order of the force between them is found to be (lnR/{xi}-1/2)/R{sup 3}, in contrast to 1/R between vortices placed in the same component. We derive it analytically using the Abrikosov ansatz and the profile functions of the vortices, confirmed numerically with the Gross-Pitaevskii model. We also find that the short-range cutoff of the intervortex potential linearly depends on the healing length.

Baryonic Bound State of Vortices in Multicomponent Superconductors

We construct a bound state of three 1/3-quantized Josephson coupled vortices in three-component superconductors with intrinsic Josephson couplings, which may be relevant with regard to iron-based superconductors. We find a Y-shaped junction of three domain walls connecting the three vortices, resembling the baryonic bound state of three quarks in QCD. The appearance of the Y-junction (but not a Δ-junction) implies that in both cases of superconductors and QCD, the bound state is described by a genuine three-body interaction (but not by the sum of two-body interactions). We also discuss a confinement/deconfinement phase transition.

Confined Monopoles Induced by Quantum Effects in Dense QCD

We analytically show that mesonic bound states of confined monopoles appear inside a non-Abelian vortex string in massless three-flavor QCD at large quark chemical potential {mu}. The orientational modes CP{sup 2} in the internal space of a vortex is described by the low-energy effective world-sheet theory. Mesons of confined monopoles are dynamically generated as bound states of kinks by the quantum effects in the effective theory. The mass of monopoles is shown to be an exponentially soft scale M{approx}{Delta}exp[-c({mu}/{Delta}){sup 2}], with the color superconducting gap {Delta} and some constant c. A possible quark-monopole duality between the hadron phase and the color superconducting phase is also discussed.

Dynamics of Non-Abelian Vortices

Scattering is studied using a moduli space metric for well-separated vortices of non-Abelian vortices in

Group theory of non-Abelian vortices

(2+1)