1,440 research outputs found
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
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
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
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
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
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
Structurally Parameterized d-Scattered Set
In -Scattered Set we are given an (edge-weighted) graph and are asked to
select at least vertices, so that the distance between any pair is at least
, thus generalizing Independent Set. We provide upper and lower bounds on
the complexity of this problem with respect to various standard graph
parameters. In particular, we show the following:
- For any , an -time algorithm, where
is the treewidth of the input graph.
- A tight SETH-based lower bound matching this algorithm's performance. These
generalize known results for Independent Set.
- -Scattered Set is W[1]-hard parameterized by vertex cover (for
edge-weighted graphs), or feedback vertex set (for unweighted graphs), even if
is an additional parameter.
- A single-exponential algorithm parameterized by vertex cover for unweighted
graphs, complementing the above-mentioned hardness.
- A -time algorithm parameterized by tree-depth
(), as well as a matching ETH-based lower bound, both for
unweighted graphs.
We complement these mostly negative results by providing an FPT approximation
scheme parameterized by treewidth. In particular, we give an algorithm which,
for any error parameter , runs in time
and returns a
-scattered set of size , if a -scattered set of the same
size exists
Quantum SUSY Algebra of -lumps in the Massive Grassmannian Sigma Model
We compute the SUSY algebra of the massive Grassmannian sigma
model in 2+1 dimensions. We first rederive the action of the model by using the
Scherk-Schwarz dimensional reduction from theory in 3+1
dimensions. Then, we perform the canonical quantization by using the Dirac
method. We find that a particular choice of the operator ordering yields the
quantum SUSY algebra of the -lumps with cental extension.Comment: 7 pages, references adde
Vortices and Monopoles in Mass-deformed SO and USp Gauge Theories
Effects of mass deformations on 1/2 Bogomol'nyi-Prasad-Sommerfield (BPS)
non-Abelian vortices are studied in 4d N=2 supersymmetric U(1) \times SO(2n)
and U(1) \times USp(2n) gauge theories, with Nf=2n quark multiplets. The 2d
N=(2,2) effective worldsheet sigma models on the Hermitian symmetric spaces
SO(2n)/U(n) and USp(2n)/U(n) found recently which describe the low-energy
excitations of the orientational moduli of the vortices, are generalized to the
respective massive sigma models. The continuous vortex moduli spaces are
replaced by a finite number (2^{n-1} or 2^{n}) of vortex solutions. The 1/2 BPS
kinks connecting different vortex vacua are magnetic monopoles in the 4d
theory, trapped inside the vortex core, with total configurations being 1/4 BPS
composite states. These configurations are systematically studied within the
semi-classical regime.Comment: 55 pages, 7 figure
Radio-frequency operation of a double-island single-electron transistor
We present results on a double-island single-electron transistor (DISET)
operated at radio-frequency (rf) for fast and highly sensitive detection of
charge motion in the solid state. Using an intuitive definition for the charge
sensitivity, we compare a DISET to a conventional single-electron transistor
(SET). We find that a DISET can be more sensitive than a SET for identical,
minimum device resistances in the Coulomb blockade regime. This is of
particular importance for rf operation where ideal impedance matching to 50 Ohm
transmission lines is only possible for a limited range of device resistances.
We report a charge sensitivity of 5.6E-6 e/sqrt(Hz) for a rf-DISET, together
with a demonstration of single-shot detection of small (<=0.1e) charge signals
on microsecond timescales.Comment: 6 pages, 6 figure
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