Fractional and semi-local non-Abelian Chern-Simons vortices

In this paper we study fractional as well as semi-local Chern-Simons vortices in G = U(1) x SO(2M) and G = U(1) x USp(2M) theories. The master equations are solved numerically using appropriate Ansatze for the moduli matrix field. In the fractional case the vortices are solved in the transverse plane due to the broken axial symmetry of the configurations (i.e. they are non-rotational invariant). It is shown that unless the fractional vortex-centers are all coincident (i.e. local case) the ring-like flux structure, characteristic of Chern-Simons vortices, will become bell-like fluxes - just as those of the standard Yang-Mills vortices. The asymptotic profile functions are calculated in all cases and the effective size is identified.Comment: LaTeX, 38 pages, 16 figures

Trions in 1+1 dimensions

We consider an Abelian BF-Higgs theory with Nf=2 Higgs fields in 1+1 dimensions. We derive a new BPS-like bound and find topological solitons with tri-charges (topological charge, Q-charge and electric charge). We call them "trions."Comment: 11 pages, 2 figures, a reference added, minor change

Enhancement of Kondo effect in multilevel quantum dots

We theoretically study enhancement mechanisms of the Kondo effect in multilevel quantum dots. In quantum dots fabricated on semiconductors, the energy difference between discrete levels \Delta is tunable by applying a magnetic field. With two orbitals and spin 1/2 in the quantum dots, we evaluate the Kondo temperature T_K as a function of \Delta, using the scaling method. T_K is maximal around \Delta=0 and decreases with increasing |\Delta|, following a power law, T_K(\Delta)=T_K(0) (T_K(0)/|\Delta|)^\gamma, which is understood as a crossover from SU(4) to SU(2) Kondo effect. The exponents on both sides of a level crossing, \gamma_L and \gamma_R, satisfy a relation of \gamma_L \gamma_R=1. We compare this enhanced Kondo effect with that by spin-singlet-triplet degeneracy for an even number of electrons, to explain recent experimental results using vertical quantum dots.Comment: 15 pages, 6 figure

Non-integrability of Self-dual Yang-Mills-Higgs System

We examine integrability of self-dual Yang-Mills system in the Higgs phase, with taking simpler cases of vortices and domain walls. We show that the vortex equations and the domain-wall equations do not have Painleve property. This fact suggests that these equations are not integrable.Comment: 15 pages, no figures, v2: references added, v3: typos corrected, the final version to appear in NP

Non-Abelian Sine-Gordon Solitons: Correspondence between SU(N)SU(N) Skyrmions and CPN−1{\mathbb C}P^{N-1} Lumps

Topologically stable non-Abelian sine-Gordon solitons have been found recently in the $U(N)$ chiral Lagrangian and a $U(N)$ gauge theory with two $N$ by $N$ complex scalar fields coupled to each other. We construct the effective theory on a non-Abelian sine-Gordon soliton that is a nonlinear sigma model with the target space ${\mathbb R} \times {\mathbb C}P^{N-1}$. We then show that ${\mathbb C}P^{N-1}$ lumps on it represent $SU(N)$ Skyrmions in the bulk point of view, providing a physical realization of the rational map Ansatz for Skyrmions of the translational (Donaldson) type. We find therefore that Skyrmions can exist stably without the Skyrme term.Comment: 24 pages, 4 figures, published versio

Statistical Mechanics of Vortices from D-branes and T-duality

We propose a novel and simple method to compute the partition function of statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs model and its non-Abelian extension on a torus. We use a D-brane realization of the vortices and T-duality relation to domain walls. We there use a special limit where domain walls reduce to gas of hard (soft) one-dimensional rods for Abelian (non-Abelian) cases. In the simpler cases of the Abelian-Higgs model on a torus, our results agree with exact results which are geometrically derived by an explicit integration over the moduli space of vortices. The equation of state for U(N) gauge theory deviates from van der Waals one, and the second virial coefficient is proportional to 1/sqrt{N}, implying that non-Abelian vortices are "softer" than Abelian vortices. Vortices on a sphere are also briefly discussed.Comment: 20 pages, 18 figure

Semilocal Fractional Instantons

We find semi-local fractional instantons of codimension four in Abelian and non-Abelian gauge theories coupled with scalar fields and the corresponding ${\mathbb C}P^{N-1}$ and Grassmann sigma models at strong gauge coupling. They are 1/4 BPS states in supersymmetric theories with eight supercharges, carry fractional (half) instanton charges characterized by the fourth homotopy group $\pi_4 (G/H)$, and have divergent energy in infinite spaces. We construct exact solutions for the sigma models and numerical solutions for the gauge theories. Small instanton singularity in sigma models is resolved at finite gauge coupling (for the Abelian gauge theory). Instantons in Abelian and non-Abelian gauge theories have negative and positive instantons charges, respectively, which are related by the Seiberg-like duality that changes the sign of the instanton charge.Comment: 20 pages, 10 figures, published version with minor change

Generation of spin-polarized current using multi-terminated quantum dot with spin-orbit interaction

We theoretically examine generation of spin-polarized current using multi-terminated quantum dot with spin-orbit interaction. First, a two-level quantum dot is analyzed as a minimal model, which is connected to $N$ ($\ge 2$) external leads via tunnel barriers. When an unpolarized current is injected to the quantum dot from a lead, a polarized current is ejected to others, similarly to the spin Hall effect. In the absence of magnetic field, the generation of spin-polarized current requires $N \ge 3$. The polarization is markedly enhanced by resonant tunneling when the level spacing in the quantum dot is smaller than the level broadening due to the tunnel coupling to the leads. In a weak magnetic field, the orbital magnetization creates a spin-polarized current even in the two-terminal geometry (N=2). The numerical study for generalized situations confirms our analytical result using the two-level model

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