485 research outputs found
't Hooft Operators in the Boundary
We consider a topologically twisted maximally supersymmetric Yang-Mills
theory on a four-manifold of the form . 't Hooft
disorder operators localized in the boundary component at finite distance of
are relevant for the study of knot theory on the three-manifold , and
have recently been constructed for a gauge group of rank one. We extend this
construction to an arbitrary gauge group . For certain values of the
magnetic charge of the 't Hooft operator, the solutions are obtained by
embedding the rank one solutions in and can be given in closed form.Comment: 9 page
Algebraic methods in the theory of generalized Harish-Chandra modules
This paper is a review of results on generalized Harish-Chandra modules in
the framework of cohomological induction. The main results, obtained during the
last 10 years, concern the structure of the fundamental series of
modules, where is a semisimple Lie
algebra and is an arbitrary algebraic reductive in
subalgebra. These results lead to a classification of simple
modules of finite type with generic minimal
types, which we state. We establish a new result about the
Fernando-Kac subalgebra of a fundamental series module. In addition, we pay
special attention to the case when is an eligible subalgebra
(see the definition in section 4) in which we prove stronger versions of our
main results. If is eligible, the fundamental series of
modules yields a natural algebraic generalization
of Harish-Chandra's discrete series modules.Comment: Keywords : generalized Harish-Chandra module, (g,k)-module of finite
type, minimal k-type, Fernando-Kac subalgebra, eligible subalgebra; Pages no.
: 13; Bibliography : 21 item
Four-qubit entanglement from string theory
We invoke the black hole/qubit correspondence to derive the classification of
four-qubit entanglement. The U-duality orbits resulting from timelike reduction
of string theory from D=4 to D=3 yield 31 entanglement families, which reduce
to nine up to permutation of the four qubits.Comment: 4 pages, 1 figure, 2 tables, revtex; minor corrections, references
adde
Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices
This paper is mainly a review of the multi--Hamiltonian nature of Toda and
generalized Toda lattices corresponding to the classical simple Lie groups but
it includes also some new results. The areas investigated include master
symmetries, recursion operators, higher Poisson brackets, invariants and group
symmetries for the systems. In addition to the positive hierarchy we also
consider the negative hierarchy which is crucial in establishing the
bi--Hamiltonian structure for each particular simple Lie group. Finally, we
include some results on point and Noether symmetries and an interesting
connection with the exponents of simple Lie groups. The case of exceptional
simple Lie groups is still an open problem.Comment: 65 pages, 67 reference
On all possible static spherically symmetric EYM solitons and black holes
We prove local existence and uniqueness of static spherically symmetric
solutions of the Einstein-Yang-Mills equations for any action of the rotation
group (or SU(2)) by automorphisms of a principal bundle over space-time whose
structure group is a compact semisimple Lie group G. These actions are
characterized by a vector in the Cartan subalgebra of g and are called regular
if the vector lies in the interior of a Weyl chamber. In the irregular cases
(the majority for larger gauge groups) the boundary value problem that results
for possible asymptotically flat soliton or black hole solutions is more
complicated than in the previously discussed regular cases. In particular,
there is no longer a gauge choice possible in general so that the Yang-Mills
potential can be given by just real-valued functions. We prove the local
existence of regular solutions near the singularities of the system at the
center, the black hole horizon, and at infinity, establish the parameters that
characterize these local solutions, and discuss the set of possible actions and
the numerical methods necessary to search for global solutions. That some
special global solutions exist is easily derived from the fact that su(2) is a
subalgebra of any compact semisimple Lie algebra. But the set of less trivial
global solutions remains to be explored.Comment: 26 pages, 2 figures, LaTeX, misprints corrected, 1 reference adde
On the application of radio frequency voltages to ion traps via helical resonators
Ions confined using a Paul trap require a stable, high voltage and low noise
radio frequency (RF) potential. We present a guide for the design and
construction of a helical coil resonator for a desired frequency that maximises
the quality factor for a set of experimental constraints. We provide an
in-depth analysis of the system formed from a shielded helical coil and an ion
trap by treating the system as a lumped element model. This allows us to
predict the resonant frequency and quality factor in terms of the physical
parameters of the resonator and the properties of the ion trap. We also compare
theoretical predictions with experimental data for different resonators, and
predict the voltage applied to the ion trap as a function of the Q-factor,
input power and the properties of the resonant circuit
Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian
We study the null fiber of a moment map related to dual pairs. We construct
an equivariant resolution of singularities of the null fiber, and get conormal
bundles of closed -orbits in the Lagrangian Grassmannian as the
categorical quotient. The conormal bundles thus obtained turn out to be a
resolution of singularities of the closure of nilpotent -orbits, which
is a "quotient" of the resolution of the null fiber.Comment: 17 pages; completely revised and add reference
Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
We study the local properties of a class of codimension-2 defects of the 6d
N=(2,0) theories of type J=A,D,E labeled by nilpotent orbits of a Lie algebra
\mathfrak{g}, where \mathfrak{g} is determined by J and the outer-automorphism
twist around the defect. This class is a natural generalisation of the defects
of the 6d theory of type SU(N) labeled by a Young diagram with N boxes. For any
of these defects, we determine its contribution to the dimension of the Higgs
branch, to the Coulomb branch operators and their scaling dimensions, to the 4d
central charges a and c, and to the flavour central charge k.Comment: 57 pages, LaTeX2
Multi-black holes from nilpotent Lie algebra orbits
For N \ge 2 supergravities, BPS black hole solutions preserving four
supersymmetries can be superposed linearly, leading to well defined solutions
containing an arbitrary number of such BPS black holes at arbitrary positions.
Being stationary, these solutions can be understood via associated non-linear
sigma models over pseudo-Riemaniann spaces coupled to Euclidean gravity in
three spatial dimensions. As the main result of this paper, we show that
whenever this pseudo-Riemanniann space is an irreducible symmetric space G/H*,
the most general solutions of this type can be entirely characterised and
derived from the nilpotent orbits of the associated Lie algebra Lie(G). This
technique also permits the explicit computation of non-supersymmetric extremal
solutions which cannot be obtained by truncation to N=2 supergravity theories.
For maximal supergravity, we not only recover the known BPS solutions depending
on 32 independent harmonic functions, but in addition find a set of non-BPS
solutions depending on 29 harmonic functions. While the BPS solutions can be
understood within the appropriate N=2 truncation of N=8 supergravity, the
general non-BPS solutions require the whole field content of the theory.Comment: Corrected version for publication, references adde
Cohort profile: Scottish Health and Ethnicity Linkage Study of 4.65 million people exploring ethnic variations in disease in Scotland
Many countries require health services to show that
they are meeting the needs of ethnic minority
populations. This requires data on health status,
healthcare uptake and outcomes and population
denominators. Weaknesses in routine data collection
often make such requirements difficult to meet.
Routine data sources in Scotland, as in most countries,
may not include a patient’s ethnicity. In
Scotland, the need for such data is driven by both
policy and legislation responding to rapidly increasing
ethnic diversity. Fair For All (2003), Scotland’s policy,
provides a strategic approach to improve the health of
minority ethnic groups. The UK Race Relations
(Amendment) Act (2000) placed a duty on public
bodies to promote racial equality. These mandates
are reflected in guidance on ethnic monitoring.
Appropriate service and research is undermined by
the lack of data. Ethnic variations occur in all of
Scotland’s national health priority areas, including
coronary heart disease/stroke, cancer, maternal
and child health and mental health.
In view of the mismatch between need for and
availability of data by ethnic group, Bhopal proposed
a demonstration project to explore retrospective
approaches. The project tested proposals including
name search methods, analyses by country of birth,
modelling/extrapolation from other nations’ datasets,
and linkage methods. The demonstration project concluded
that census health records linkage methods—
in the context of this project first mooted by Povey—
held most promise. To our knowledge, attempting
matching of a national health dataset to a complete
national census using demographic identifiers rather
than national identity numbers had not been reported
though health data linkage is well-established in the
UK and internationally, including exploring ethnicity
and health
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