Zero-modes of Non-Abelian Solitons in Three Dimensional Gauge Theories

We study non-Abelian solitons of the Bogomol'nyi type in N=2 (d=2+1) supersymmetric Chern-Simons (CS) and Yang-Mills (YM) theory with a generic gauge group. In CS theory, we find topological, non-topological and semi-local (non-)topological vortices of non-Abelian kinds in unbroken, broken and partially broken vacua. We calculate the number of zero-modes using an index theorem and then we apply the moduli matrix formalism to realize the moduli parameters. For the topological solitons we exhaust all the moduli while we study several examples of the non-topological and semi-local solitons. We find that the zero-modes of the topological solitons are governed by the moduli matrix H_0 only and those of the non-topological solitons are governed by both H_0 and the gauge invariant field \Omega. We prove local uniqueness of the master equation in the YM case and finally, compare all results between the CS and YM theories.Comment: 54 pages, 1 figur

Valence instability of cerium under pressure in the Kondo-like perovskite La0.1_{0.1}Ce0.4_{0.4}Sr0.5_{0.5}MnO3_3

Effect of hydrostatic pressure and magnetic field on electrical resistance of the Kondo-like perovskite manganese oxide, La$_{0.1}$Ce$_{0.4}$Sr$_{0.5}$MnO$_3$ with a ferrimagnetic ground state, have been investigated up to 2.1 GPa and 9 T. In this compound, the Mn-moments undergo double exchange mediated ferromagnetic ordering at $T_{\rm C}$ $\sim$ 280 K and there is a resistance maximum, $T_{\rm max}$ at about 130 K which is correlated with an antiferromagnetic ordering of {\it cerium} with respect to the Mn-sublattice moments. Under pressure, the $T_{\rm max}$ shifts to lower temperature at a rate of d$T_{max}$/d$P$ = -162 K/GPa and disappears at a critical pressure $P_{\rm c}$ $\sim$ 0.9 GPa. Further, the coefficient, $m$ of $-logT$ term due to Kondo scattering decreases linearly with increase of pressure showing an inflection point in the vicinity of $P_{\rm c}$. These results suggest that {\it cerium} undergoes a transition from Ce$^{3+}$ state to Ce$^{4+}$/Ce$^{3+}$ mixed valence state under pressure. In contrast to pressure effect, the applied magnetic field shifts $T_{\rm max}$ to higher temperature presumably due to enhanced ferromagnetic Mn moments.Comment: to be published in Phys. Rev. B (rapid commun

Non-Abelian vortex dynamics: Effective world-sheet action

The low-energy vortex effective action is constructed in a wide class of systems in a color-flavor locked vacuum, which generalizes the results found earlier in the context of U(N) models. It describes the weak fluctuations of the non-Abelian orientational moduli on the vortex worldsheet. For instance, for the minimum vortex in SO(2N) x U(1) or USp(2N) x U(1) gauge theories, the effective action found is a two-dimensional sigma model living on the Hermitian symmetric spaces SO(2N)/U(N) or USp(2N)/U(N), respectively. The fluctuating moduli have the structure of that of a quantum particle state in spinor representations of the GNO dual of the color-flavor SO(2N) or USp(2N) symmetry, i.e. of SO(2N) or of SO(2N+1). Applied to the benchmark U(N) model our procedure reproduces the known CP(N-1) worldsheet action; our recipe allows us to obtain also the effective vortex action for some higher-winding vortices in U(N) and SO(2N) theories.Comment: LaTeX, 25 pages, 0 figure

Vortex counting from field theory

The vortex partition function in 2d N = (2,2) U(N) gauge theory is derived from the field theoretical point of view by using the moduli matrix approach. The character for the tangent space at each moduli space fixed point is written in terms of the moduli matrix, and then the vortex partition function is obtained by applying the localization formula. We find that dealing with the fermionic zero modes is crucial to obtain the vortex partition function with the anti-fundamental and adjoint matters in addition to the fundamental chiral multiplets. The orbifold vortex partition function is also investigated from the field theoretical point of view.Comment: 21 pages, no figure

Supersymmetry Breaking on Gauged Non-Abelian Vortices

There are a large number of systems characterized by a completely broken gauge symmetry, but with an unbroken global color-flavor diagonal symmetry, i.e., systems in the so-called color-flavor locked phase. If the gauge symmetry breaking supports vortices, the latter develop non-Abelian orientational zero-modes and become non-Abelian vortices, a subject of intense study in the last several years. In this paper we consider the effects of weakly gauging the full exact global flavor symmetry in such systems, deriving an effective description of the light excitations in the presence of a vortex. Surprising consequences are shown to follow. The fluctuations of the vortex orientational modes get diffused to bulk modes through tunneling processes. When our model is embedded in a supersymmetric theory, the vortex is still 1/2 BPS saturated, but the vortex effective action breaks supersymmetry spontaneously.Comment: Latex, 24 pages, 1 figur

Vortices on Orbifolds

The Abelian and non-Abelian vortices on orbifolds are investigated based on the moduli matrix approach, which is a powerful method to deal with the BPS equation. The moduli space and the vortex collision are discussed through the moduli matrix as well as the regular space. It is also shown that a quiver structure is found in the Kahler quotient, and a half of ADHM is obtained for the vortex theory on the orbifolds as the case before orbifolding.Comment: 25 pages, 4 figures; references adde

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.Comment: 24 pages, 5 figures; v2: typos corrected, references added, minor changes; v3: published versio

Resonant tunneling and Fano resonance in quantum dots with electron-phonon interaction

We theoretically study the resonant tunneling and Fano resonance in quantum dots with electron-phonon (e-ph) interaction. We examine the bias-voltage ($V$) dependence of the decoherence, using Keldysh Green function method and perturbation with respect to the e-ph interaction. With optical phonons of energy $\omega_0$, only the elastic process takes place when $eV<\omega_0$, in which electrons emit and absorb phonons virtually. The process suppresses the resonant amplitude. When $eV>\omega_0$, the inelastic process is possible which is accompanied by real emission of phonons. It results in the dephasing and broadens the resonant width. The bias-voltage dependence of the decoherence cannot be obtained by the canonical transformation method to consider the e-ph interaction if its effect on the tunnel coupling is neglected. With acoustic phonons, the asymmetric shape of the Fano resonance grows like a symmetric one as the bias voltage increases, in qualitative accordance with experimental results.Comment: 28 pages, 11 figure

Kondo Effect in Multiple-Dot Systems

We study the Kondo effect in multiple-dot systems for which the inter- as well as intra-dot Coulomb repulsions are strong, and the inter-dot tunneling is small. The application of the Ward-Takahashi identity to the inter-dot dynamical susceptibility enables us to analytically calculate the conductance for a double-dot system by using the Bethe-ansatz exact solution of the SU(4) impurity Anderson model. It is clarified how the inter-dot Kondo effect enhances or suppresses the conductance under the control of the gate voltage and the magnetic field. We then extend our analysis to multiple-dot systems including more than two dots, and discuss their characteristic transport properties by taking a triple-dot system as an example.Comment: 8 pages, 9 figure

Phonon Spectroscopy by Electric Measurements of Coupled Quantum Dots

We propose phonon spectroscopy by electric measurements of the low-temperature conductance of coupled-quantum dots, specifically employing dephasing of the quantum electronic transport by the phonons. The setup we consider consists of a T-shaped double-quantum-dot (DQD) system in which only one of the dots (dot 1) is connected to external leads and the other (dot 2) is coupled solely to the first one. For noninteracting electrons, the differential conductance of such a system vanishes at a voltage located in-between the energies of the bonding and the anti-bonding states, due to destructive interference. When electron-phonon (e-ph) on the DQD is invoked, we find that, at low temperatures, phonon emission taking place on dot 1 does not affect the interference, while phonon emission from dot 2 suppresses it. The amount of this suppression, as a function of the bias voltage, follows the effective e-ph coupling reflecting the phonon density of states and can be used for phonon spectroscopy.Comment: 9 pages, 6 figure