Minoru Eto

We review our recent work on solitons in the Higgs phase. We use U(N_C) gauge theory with N_F Higgs scalar fields in the fundamental representation, which can be extended to possess eight supercharges. We propose the moduli matrix as a fundamental tool to exhaust all BPS solutions, and to characterize all possible moduli parameters. Moduli spaces of domain walls (kinks) and vortices, which are the only elementary solitons in the Higgs phase, are found in terms of the moduli matrix. Stable monopo

We completely determine the moduli space M(N,k) of k vortices in U(N) gauge theory with N Higgs fields in the fundamental representation. Its open subset for separated vortices is found as the symmetric product (CxCP(N-1))k/(see text)k. Orbifold singularities of this space correspond to coincident vortices and are resolved resulting in a smooth moduli manifold. The relation to Kähler quotient construction is discussed.

When instantons are put into the Higgs phase, vortices are attached to instantons. We construct such composite solitons as $1/4$ BPS states in five-dimensional supersymmetric $U({N}_{\mathrm{C}})$ gauge theory with ${N}_{\mathrm{F}}(\ensuremath{\ge}{N}_{\mathrm{C}})$ fundamental hypermultiplets. We solve the hypermultiplet BPS equation and show that all $1/4$ BPS solutions are generated by an ${N}_{\mathrm{C}}\ifmmode\times\else\texttimes\fi{}{N}_{\mathrm{F}}$ matrix which is holomorphic in two

We make a detailed study of the moduli space of winding number two ($k=2$) axially symmetric vortices (or equivalently, of coaxial composite of two fundamental vortices), occurring in $U(2)$ gauge theory with two flavors in the Higgs phase, recently discussed by Hashimoto and Tong and by Auzzi, Shifman, and Yung. We find that it is a weighted projective space $W\mathbf{C}{P}_{(2,1,1)}^{2}\ensuremath{\simeq}\mathbf{C}{P}^{2}/{\mathbf{Z}}_{2}$. This manifold contains an ${A}_{1}$-type (${\mathbf{Z

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 $(\mathrm{ln}R/\ensuremath{\xi}\ensuremath{-}1/2)/{R}^{3}$, 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

We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings.

We study Bogomol'nyi-Prasad-Sommerfield (BPS) non-Abelian semilocal vortices in $U({N}_{\mathrm{C}})$ gauge theory with ${N}_{\mathrm{F}}$ flavors, ${N}_{\mathrm{F}}>{N}_{\mathrm{C}}$, in the Higgs phase. The moduli space for an arbitrary winding number is described using the moduli matrix formalism. We find a relation between the moduli spaces of the semilocal vortices in Seiberg-like dual pairs of theories, $U({N}_{\mathrm{C}})$ and $U({N}_{\mathrm{F}}\ensuremath{-}{N}_{\mathrm{C}})$. They

We investigate vortices on a cylinder in supersymmetric non-Abelian gauge theory with hypermultiplets in the fundamental representation. We identify moduli space of periodic vortices and find that a pair of wall-like objects appears as the vortex moduli is varied. Usual domain walls also can be obtained from the single vortex on the cylinder by introducing a twisted boundary condition. We can understand these phenomena as a $T$ duality among D-brane configurations in type II superstring theories

A systematic method to obtain the effective Lagrangian on the Bogomol'nyi-Prasad-Sommerfield background in supersymmetric gauge theories is worked out, taking domain walls and vortices as concrete examples. The Lagrangian in terms of the superfields with four preserved supercharges is expanded in powers of the slow-movement parameter $\ensuremath{\lambda}$. The expansion gives the superfield form of the Bogomol'nyi-Prasad-Sommerfield equations at $\mathcal{O}({\ensuremath{\lambda}}^{0})$, and al

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)ex

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 diff

Supersymmetric $U({N}_{\mathrm{C}})$ gauge theory with ${N}_{\mathrm{F}}$ massive hypermultiplets in the fundamental representation is given by the brane configuration made of ${N}_{\mathrm{C}}$ fractional $\mathrm{D}p$-branes stuck at the ${\mathbf{Z}}_{2}$ orbifold singularity on ${N}_{\mathrm{F}}$ separated $\mathrm{D}(p+4)$-branes. We show that non-Abelian walls in this theory are realized as kinky fractional $\mathrm{D}p$-branes interpolating between $\mathrm{D}(p+4)$-branes. Wall solutions

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-e

Some years ago, Atiyah and Manton described a method to construct approximate Skyrmion solutions from Yang-Mills instantons. Here we present a dynamical realization of this construction using domain walls in a five-dimensional gauge theory. The non-Abelian gauge symmetry is broken in each vacuum but restored in the core of the domain wall, allowing instantons to nestle inside the wall. We show that the world volume dynamics of the wall is given by the Skyrme model, including the four-derivative