Witten effect in a crystalline topological insulator

It has been noted a long time ago that a term of the form theta (e^2/2\pi h) B dot E may be added to the standard Maxwell Lagrangian without modifying the familiar laws of electricity and magnetism. theta is known to particle physicists as the 'axion' field and whether or not it has a nonzero expectation value in vacuum remains a fundamental open question of the Standard Model. A key manifestation of the axion term is the Witten effect: a unit magnetic monopole placed inside a medium with non-zero theta is predicted to bind a (generally fractional) electric charge -e(theta/2 pi+n) with n integer. Here we conduct a first test of the Witten effect, based on the recently established fact that the axion term with theta=pi emerges naturally in the description of the electromagnetic response of a new class of crystalline solids called topological insulators - materials distinguished by strong spin-orbit coupling and non-trivial band structure. Using a simple physical model for a topological insulator, we demonstrate the existence of a fractional charge bound to a monopole by an explicit numerical calculation. We also propose a scheme for generating an 'artificial' magnetic monopole in a topological insulator film, that may be used to facilitate the first experimental test of Witten's prediction.Comment: 7 pages, 2 figures. Version to appear in PRB; minor changes, discussion of several issues expande

Axially symmetric Yang-Mills-Higgs solutions in AdS spacetime

We consider axially symmetric solutions of SU(2) Yang-Mills-Higgs theory in globally AdS spacetime and a fixed Schwarzschild-AdS black hole background. The solutions are characterized by two integers $(m,n)$ where $m$ is related to the polar angle and $n$ to the azimuthal angle. Two types of finite energy, regular configurations are considered: solutions with net magnetic charge $n>1$ and monopole-antimonopole pairs and chains with zero net magnetic charge. The configurations are endowed with an electric charge and carry also a nonvanishing angular momentum density.Comment: 13 pages, 3 figure

Embedded monopoles in quark eigenmodes in SU(2) Yang-Mills Theory

We study the embedded QCD monopoles (``quark monopoles'') using low-lying eigenmodes of the overlap Dirac operator in zero- and finite-temperature SU(2) Yang-Mills theory on the lattice. These monopoles correspond to the gauge-invariant hedgehogs in the quark-antiquark condensates. The monopoles were suggested to be agents of the chiral symmetry restoration since their cores should suppress the chiral condensate. We study numerically the scalar, axial and chirally invariant definitions of the embedded monopoles and show that the monopole densities are in fact globally anti-correlated with the density of the Dirac eigenmodes. We observe, that the embedded monopoles corresponding to low-lying Dirac eigenvalues are dense in the chirally invariant (high temperature) phase and dilute in the chirally broken (low temperature) phase. We find that the scaling of the scalar and axial monopole densities towards the continuum limit is similar to the scaling of the string-like objects while the chirally invariant monopoles scale as membranes. The excess of gluon energy at monopole positions reveals that the embedded QCD monopole possesses a gluonic core, which is, however, empty at the very center of the monopole.Comment: 29 pages, 27 figures, RevTeX 4.0; revised to match the published version (clarifying remarks, references and acknowledgments are added

Oscillons in gapless theories

We show that large scale oscillons, i.e., quasiperiodic, long-living particlelike solutions, may exist in massless theories, too. Their existence is explained using an effective (smeared) mass threshold which takesinto account nonlinear (finite) perturbations

Twisted toroidal vortex-solitons in inhomogeneous media with repulsive nonlinearity

Toroidal modes in the form of so-called Hopfions, with two independent winding numbers, a hidden one (twist, s), which characterizes a circular vortex thread embedded into a three-dimensional soliton, and the vorticity around the vertical axis m, appear in many fields, including the field theory, ferromagnetics, and semi- and superconductors. Such topological states are normally generated in multi-component systems, or as trapped quasi-linear modes in toroidal potentials. We uncover that stable solitons with this structure can be created, without any linear potential, in the single-component setting with the strength of repulsive nonlinearity growing fast enough from the center to the periphery, for both steep and smooth modulation profiles. Toroidal modes with s=1 and vorticity m=0,1,2 are produced. They are stable for m<=1, and do not exist for s>1. An approximate analytical solution is obtained for the twisted ring with s=1, m=0. Under the application of an external torque, it rotates like a solid ring. The setting can be implemented in BEC, by means of the Feshbach resonance controlled by inhomogene-ous magnetic fields.Comment: 12 pages, 5 figures, to appear in Physical Review Letter

Electric Flux Tube in Magnetic Plasma

In this paper we study a methodical problem related to the magnetic scenario recently suggested and initiated by the authors \cite{Liao_ES_mono} to understand the strongly coupled quark-gluon plasma (sQGP): the electric flux tube in monopole plasma. A macroscopic approach, interpolating between Bose condensed (dual superconductor) and classical gas medium is developed first. Then we work out a microscopic approach based on detailed quantum mechanical calculation of the monopole scattering on electric flux tube, evaluating induced currents for all partial waves. As expected, the flux tube looses its stability when particles can penetrate it: we make this condition precise by calculating the critical value for the product of the flux tube size times the particle momentum, above which the flux tube dissolves. Lattice static potentials indicate that flux tubes seem to dissolve at $T>T_{dissolution} \approx 1.3 T_c$. Using our criterion one gets an estimate of the magnetic density $n\approx 4.4 \sim 6.6 fm^{-3}$ at this temperature.Comment: New version with new referecences added and minor changes. 15 pages, 8 figure

Chains of Boson Stars

We study axially symmetric multi-soliton solutions of a complex scalar field theory with a sextic potential, minimally coupled to Einstein's gravity. These solutions carry no angular momentum and can be classified by the number of nodes of the scalar field, $k_z$, along the symmetry axis; they are interpreted as chains with $k_z+1$ boson stars, bound by gravity, but kept apart by repulsive scalar interactions. Chains with an odd number of constituents show a spiraling behavior for their ADM mass (and Noether charge) in terms of their angular frequency, similarly to a single fundamental boson star, as long as the gravitational coupling is small; for larger coupling, however, the inner part of the spiral is replaced by a merging with the fundamental branch of radially excited spherical boson stars. Chains with an even number of constituents exhibit a truncated spiral pattern, with only two or three branches, ending at a limiting solution with finite values of ADM mass and Noether charge.Comment: 20 pages, 6 figure

Radiation of an electric charge in the field of a magnetic monopole

We consider the radiation of photons from quarks scattering on color-magnetic monopoles in the Quark-Gluon Plasma. We consider a temperature regime T\gsim2T_c, where monopoles can be considered as static, rare objects embedded into matter consisting mostly of the usual "electric" quasiparticles, quarks and gluons. The calculation is performed in the classical, non-relativistic approximation and results are compared to photon emission from Coulomb scattering of quarks, known to provide a significant contribution to the photon emission rates from QGP. The present study is a first step towards understanding whether this scattering process can give a sizeable contribution to dilepton production in heavy-ion collisions. Our results are encouraging: by comparing the magnitudes of the photon emission rate for the two processes, we find a dominance in the case of quark-monopole scattering. Our results display strong sensitivity to finite densities of quarks and monopoles.Comment: 28 pages, 8 figure

Multikink scattering in the ϕ6 model revisited

Antikink-kink (KK) collisions in the ¯ ϕ6 model exhibit resonant scattering although the ϕ6 kinks do not support any bound states to which energy could be transferred. In P. Dorey et al. [Kink-Antikink Collisions in the ϕ6 Model, Phys. Rev. Lett. 107, 091602 (2011)] it was conjectured that, instead, energy is transferred to a collective bound mode of the full KK configuration. Here we present further strong evidence for this ¯ conjecture. Further, we construct a collective coordinate model (CCM) for KK scattering based on this ¯ collective bound mode trapped between the KK pair which allows us to reproduce the full dynamics of ¯ KK¯ scattering with striking accuracy. We also study kink-antikink (KK) scattering and its description by a ¯ CCM. In this case a significant role of radiation is discovered