Color Magnetic Flux Tubes Research Articles

On transverse momentum broadening in real-time lattice simulations of the glasma and in the weak-field limit

In these proceedings, we report on our numerical lattice simulations of partons traversing the boost-invariant, non-perturbative glasma as created at the early stages of collisions at RHIC and LHC. Since these highly energetic partons are produced from hard scatterings during heavy-ion collisions, they are already affected by the first stage of the medium's time evolution, the glasma, which is the pre-equilibrium precursor state of the quark-gluon plasma. We find that partons quickly accumulate transverse momentum up to the saturation momentum during the glasma stage. Moreover, we observe an interesting anisotropy in transverse momentum broadening of partons with larger broadening in the rapidity than in the azimuthal direction. Its origin can be related to correlations among the longitudinal color-electric and color-magnetic flux tubes in the initial state of the glasma. We compare these observations to the semi-analytic results obtained by a weak-field approximation, where we also find such an anisotropy in a parton's transverse momentum broadening.

Chiral non-Abelian vortices and their confinement in three flavor dense QCD

We find chiral non-Abelian vortices having windings only in one of the diquark condensations of left-handed and right-handed quarks in the color-flavor locked phase of dense QCD. They are the minimum vortices carrying half color magnetic fluxes of those of non-Abelian semi-superfluid vortices (color magnetic flux tubes) and 1/6 quantized superfluid circulations of Abelian superfluid vortices. These vortices carry ${\mathbb C}P^2$ orientational moduli in the internal space corresponding to their fluxes. The ${\mathbb C}P^2$ moduli of two chiral non-Abelian vortices with chiralities opposite to each other are energetically favored to be aligned while those of a vortex and anti-vortex to be orthogonal, and then these vortices attract each other. They are attached by chiral domain walls in the presence of the mass and axial anomaly terms explicitly breaking axial and chiral symmetries. We numerically show that two chiral non-Abelian vortices with chiralities opposite to each other are connected by a chiral domain wall, consisting a mesonic bound state which is nothing but a non-Abelian semi-superfluid vortex. We also show that Abelian and non-Abelian axial vortices attached by chiral domain walls are all unstable to decay into a set of chiral non-Abelian vortices. Furthermore, we find that chiral non-Abelian vortices exhibit unique features: one is the so-called topological obstruction implying that unbroken symmetry generators in the bulk are not defined globally around the vortices, and the other is color non-singlet Aharonov-Bohm (AB) phases implying that quarks encircling these vortices can detect the colors of magnetic fluxes of them at infinite distances.

New color-magnetic defects in dense quark matter

Color-flavor locked (CFL) quark matter expels color-magnetic fields due to the Meissner effect. One of these fields carries an admixture of the ordinary abelian magnetic field and therefore flux tubes may form if CFL matter is exposed to a magnetic field, possibly in the interior of neutron stars or in quark stars. We employ a Ginzburg–Landau approach for three massless quark flavors, which takes into account the multi-component nature of color superconductivity. Based on the weak-coupling expressions for the Ginzburg–Landau parameters, we identify the regime where CFL is a type-II color superconductor and compute the radial profiles of different color-magnetic flux tubes. Among the configurations without baryon circulation we find a new solution that is energetically preferred over the flux tubes previously discussed in the literature in the parameter regime relevant for compact stars. Within the same setup, we also find a new defect in the 2SC phase, namely magnetic domain walls, which emerge naturally from the previously studied flux tubes if a more general ansatz for the order parameter is used. Color-magnetic defects in the interior of compact stars allow for sustained deformations of the star, potentially strong enough to produce detectable gravitational waves.

Low-energy effective worldsheet theory of a non-Abelian vortex in high-density QCD revisited: A regular gauge construction

Color symmetry is spontaneously broken in quark matter at high density as a consequence of di-quark condensations with exhibiting color superconductivity. Non-Abelian vortices or color magnetic flux tubes stably exist in the color-flavor locked phase at asymptotically high-density. The effective worldsheet theory of a single non-Abelian vortex was previously calculated in the singular gauge to obtain the ${\mathbb C}P^2$ model [ arXiv:0908.4470 , arXiv:0912.1352 ]. Here, we reconstruct the effective theory in a regular gauge without taking a singular gauge, confirming the previous results in the singular gauge. As a byproduct of our analysis, we find that non-Abelian vortices in high-density QCD do not suffer from any obstruction for the global definition of a symmetry breaking.

Aharonov-Bohm phase in high density quark matter

Stable non-Abelian vortices, which are color magnetic flux tubes as well as superfluid vortices, are present in the color-flavor locked phase of dense quark matter with diquark condensations. We calculate the Aharanov-Bohm phases of charged particles, that is, electrons, muons, and color-flavor locked mesons made of tetraquarks around a non-Abelian vortex.

Coupling between Majorana fermions and Nambu-Goldstone bosons inside a non-Abelian vortex in dense QCD

Quark matter at high density may exhibit color superconductivity. As magnetic flux tubes in metallic superconductors, color magnetic flux tubes as non-Abelian vortices appear in the color-flavor locked phase of high density QCD. ${\mathbb C}P^2$ Nambu-Goldstone bosons and Majorana fermions belonging to the triplet representation are known to be localized around a non-Abelian vortex. In this paper, we determine the coupling of these bosonic and fermionic modes by using the nonlinear realization method.

Vortices and other topological solitons in dense quark matter

Abstract Dense quantum chromodynamic matter accommodates various kind of topological solitons such as vortices, domain walls, monopoles, kinks, boojums, and so on. In this review, we discuss various properties of topological solitons in dense quantum chromodynamics (QCD) and their phenomenological implications. Particular emphasis is placed on the topological solitons in the color–flavor-locked (CFL) phase, which exhibits both superfluidity and superconductivity. The properties of topological solitons are discussed in terms of effective field theories such as the Ginzburg–Landau theory, the chiral Lagrangian, or the Bogoliubov–de Gennes equation. The most fundamental string-like topological excitations in the CFL phase are non-Abelian vortices, which are 1/3 quantized superfluid vortices and color magnetic flux tubes. These vortices are created at a phase transition by the Kibble–Zurek mechanism or when the CFL phase is realized in compact stars, which rotate rapidly. The interaction between vortices is found to be repulsive and consequently a vortex lattice is formed in rotating CFL matter. Bosonic and fermionic zero-energy modes are trapped in the core of a non-Abelian vortex and propagate along it as gapless excitations. The former consists of translational zero modes (a Kelvin mode) with a quadratic dispersion and ${\mathbb {C}}P^2$ Nambu–Goldstone gapless modes with a linear dispersion, associated with the CFL symmetry spontaneously broken in the core of a vortex, while the latter is Majorana fermion zero modes belonging to the triplet of the symmetry remaining in the core of a vortex. The low-energy effective theory of the bosonic zero modes is constructed as a non-relativistic free complex scalar field and a relativistic ${\mathbb {C}}P^2$ model in 1+1 dimensions. The effects of strange quark mass, electromagnetic interactions, and non-perturbative quantum corrections are taken into account in the ${\mathbb {C}}P^2$ effective theory. Various topological objects associated with non-Abelian vortices are studied; colorful boojums at the CFL interface, the quantum color magnetic monopole confined by vortices, which supports the notion of quark–hadron duality, and Yang–Mills instantons inside a non-Abelian vortex as lumps are discussed. The interactions between a non-Abelian vortex and quasiparticles such as phonons, gluons, mesons, and photons are studied. As a consequence of the interaction with photons, a vortex lattice behaves as a cosmic polarizer. As a remarkable consequence of Majorana fermion zero modes, non-Abelian vortices are shown to behave as a novel kind of non-Abelian anyon. In the order parameters of 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 quark matter cores of neutron stars

We argue that if color-superconducting quark matter exists in the core of a neutron star, it may contain a high density of flux tubes, carrying flux that is mostly color magnetic, with a small admixture of ordinary magnetic flux. We focus on the two-flavor color-superconducting (‘2SC’) phase, and assume that the flux tubes are energetically stable, although this has not yet been demonstrated. The density of flux tubes depends on the nature of the transition to the color-superconducting phase, and could be within an order of magnitude of the density of magnetic flux tubes that would be found if the core were superconducting nuclear matter. We calculate the cross-section for Aharonov–Bohm scattering of gapless fermions off the flux tubes, and the associated collision time and frictional force on a moving flux tube. We discuss the other forces on the flux tube, and find that if we take into account only the forces that arise within the 2SC core region, then the timescale for expulsion of the color flux tubes from the 2SC core is of order 1010 years.

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.

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. 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 wave length of the massive gluon when the gluon mass is larger than the scalar mass.

Glittering Glasmas

We compute the production of gluons from Glasma color flux tubes. We calculate the probability distribution of gluon multiplicities arising from the distribution of color electric and color magnetic flux tubes found in the Glasma. We show that the result corresponds to the negative binomial probability distribution observed in experiments. The parameter k that characterizes this distribution is proportional to the number of colors N c 2 − 1 and to the number of flux tubes. For one gluon color and one flux tube, the multiplicity distribution is close to a Bose–Einstein distribution. We call this decay process “Glitter”, a term that is explained below.

On the QCD Vacuum

A review of a class of color magnetic vacuum models is given. It is shown how the instability of a homogeneous color magnetic field leads to the formation of domains, which have the form of flux tubes. It is argued that energy is gained by having a quantum liquid state of color magnetic flux tubes. Various numerical estimates are summarized.

A color magnetic vortex condensate in QCD

It is shown that there exists a very close analogy between a lattice of vortices in a superconductor near the critical field and a condensate of color magnetic flux tubes due to the unstable mode in QCD. This analogy makes it possible to identify a dynamical Higgs field in QCD. We show that the color magnetic flux tubes are quantized in terms of the center group Z(2) in the SU(2) case. In the case of SU( N) it is possible to select a color direction of the field such that one has Z( N) quantization.

On the formation of a random color magnetic quantum liquid in QCD

It is shown that a quantum state consisting of a condensate of color magnetic flux tubes is formed in QCD for a rather weak coupling g 2/4 π = 0.37. This result is obtained in a systematic search for energy minimizing forms of the QCD unstable magnetic mode. The magnetic field is argued to be of a “random” type with 〈 H〉 = 0 and 〈 H 2〉 ≠ 0 at any point.