1,683 research outputs found

### 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

### Group Theory of Non-Abelian Vortices

We investigate the structure of the moduli space of multiple BPS non-Abelian
vortices in U(N) gauge theory with N fundamental Higgs fields, focusing our
attention on the action of the exact global (color-flavor diagonal) SU(N)
symmetry on it. The moduli space of a single non-Abelian vortex, CP(N-1), is
spanned by a vector in the fundamental representation of the global SU(N)
symmetry. The moduli space of winding-number k vortices is instead spanned by
vectors in the direct-product representation: they decompose into the sum of
irreducible representations each of which is associated with a Young tableau
made of k boxes, in a way somewhat similar to the standard group composition
rule of SU(N) multiplets. The K\"ahler potential is exactly determined in each
moduli subspace, corresponding to an irreducible SU(N) orbit of the
highest-weight configuration.Comment: LaTeX 46 pages, 4 figure

### Electronic States in Silicon Quantum Dots: Multivalley Artificial Atoms

Electronic states in silicon quantum dots are examined theoretically, taking
into account a multivalley structure of the conduction band. We find that (i)
exchange interaction hardly works between electrons in different valleys. In
consequence electrons occupy the lowest level in different valleys in the
absence of Hund's coupling when the dot size is less than 10 nm. High-spin
states are easily realized by applying a small magnetic field. (ii) When the
dot size is much larger, the electron-electron interaction becomes relevant in
determining the electronic states. Electrons are accommodated in a valley,
making the highest spin, to gain the exchange energy. (iii) In the presence of
intervalley scattering, degenerate levels in different valleys are split. This
could result in low-spin states. These spin states in multivalley artificial
atoms can be observed by looking at the magnetic-field dependence of peak
positions in the Coulomb oscillation.Comment: 18 pages, 5 figure

### Type I Non-Abelian Superconductors in Supersymmetric Gauge Theories

Non-BPS non-Abelian vortices with CP^1 internal moduli space are studied in
an N=2 supersymmetric U(1) x SU(2) gauge theory with softly breaking adjoint
mass terms. For generic internal orientations the classical force between two
vortices can be attractive or repulsive. On the other hand, the mass of the
scalars in the theory is always less than that of the vector bosons; also, the
force between two vortices with the same CP^1 orientation is always attractive:
for these reasons we interpret our model as a non-Abelian generalization of
type I superconductors. We compute the effective potential in the limit of two
well separated vortices. It is a function of the distance and of the relative
colour-flavour orientation of the two vortices; in this limit we find an
effective description in terms of two interacting CP^1 sigma models. In the
limit of two coincident vortices we find two different solutions with the same
topological winding and, for generic values of the parameters, different
tensions. One of the two solutions is described by a CP^1 effective sigma
model, while the other is just an Abelian vortex without internal degrees of
freedom. For generic values of the parameters, one of the two solutions is
metastable, while there are evidences that the other one is truly stable.Comment: 35 pages, 8 figures. v2: fixed typos and added small comments, v3
removed an unecessary figur

### 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

### Solitons in Supersymmety Breaking Meta-Stable Vacua

In recently found supersymmetry-breaking meta-stable vacua of the
supersymmetric QCD, we examine possible exsitence of solitons. Homotopy groups
of the moduli space of the meta-stable vacua show that there is no nontrivial
soliton for SU(N_c) gauge group. When U(1)_B symmetry present in the theory is
gauged, we find non-BPS solitonic (vortex) strings whose existence and
properties are predicted from brane configurations. We obtain explicit
classical solutions which reproduce the predicitions. For SO(N_c) gauge group,
we find there are solitonic strings for N = N_f-N_c+4 = 2, and Z_2 strings for
the other N. The strings are meta-stable as they live in the meta-stable vacua.Comment: 30 pages, 14 figures, Comments on stability of non-BPS vortices are
added, Comments on sigma model solitons are added, An appendix is adde

### 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

### QCD String as Vortex String in Seiberg-Dual Theory

We construct a classical vortex string solution in a Seiberg-dual theory of
N=1 supersymmetric SO(N_c) QCD which flows to a confining phase. We claim that
this vortex string is a QCD string, as previouly argued by M.Strassler. In
SO(N_c) QCD, it is known that stable QCD strings exist even in the presence of
dynamical quarks. We show that our vortex strings are stable in the
Seiberg-dual theory.Comment: 15 pages, 1 figur

### 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

### Static Interactions of non-Abelian Vortices

Interactions between non-BPS non-Abelian vortices are studied in non-Abelian
U(1) x SU(N) extensions of the Abelian-Higgs model in four dimensions. The
distinctive feature of a non-Abelian vortex is the presence of an internal
CP^{N-1} space of orientational degrees of freedom. For fine-tuned values of
the couplings, the vortices are BPS and there is no net force between two
static parallel vortices at arbitrary distance. On the other hand, for generic
values of the couplings the interactions between two vortices depend
non-trivially on their relative internal orientations. We discuss the problem
both with a numerical approach (valid for small deviations from the BPS limit)
and in a semi-analytical way (valid at large vortex separations). The
interactions can be classified with respect to their asymptotic property at
large vortex separation. In a simpler fine-tuned model, we find two regimes
which are quite similar to the usual type I/II Abelian superconductors. In the
generic model we find other two new regimes: type I*/II*. Unlike the type I
(type II) case, where the interaction is always attractive (repulsive), the
type I* and II* have both attractive and repulsive interactions depending on
the relative orientation. We have found a rich variety of interactions at small
vortex separations. For some values of the couplings, a bound state of two
static vortices at a non-zero distance exists.Comment: 36 pages, 13 figures; v2 a small comment and a reference adde

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