165,224 research outputs found
Extended supersymmetric sigma models in AdS_4 from projective superspace
There exist two superspace approaches to describe N=2 supersymmetric
nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in
terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and
arXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdS
projective-superspace techniques developed in arXiv:0807.3368. The virtue of
the approach (i) is that it makes manifest the geometric properties of the N=2
supersymmetric sigma-models in AdS_4. The target space must be a non-compact
hyperkahler manifold endowed with a Killing vector field which generates an
SO(2) group of rotations on the two-sphere of complex structures. The power of
the approach (ii) is that it allows us, in principle, to generate hyperkahler
metrics as well as to address the problem of deformations of such metrics.
Here we show how to relate the formulation (ii) to (i) by integrating out an
infinite number of N=1 AdS auxiliary superfields and performing a superfield
duality transformation. We also develop a novel description of the most general
N=2 supersymmetric nonlinear sigma-model in AdS_4 in terms of chiral
superfields on three-dimensional N=2 flat superspace without central charge.
This superspace naturally originates from a conformally flat realization for
the four-dimensional N=2 AdS superspace that makes use of Poincare coordinates
for AdS_4. This novel formulation allows us to uncover several interesting
geometric results.Comment: 88 pages; v3: typos corrected, version published in JHE
Killing symmetries of generalized Minkowski spaces. 1-Algebraic-infinitesimal structure of space-time rotation groups
In this paper, we introduce the concept of N-dimensional generalized
Minkowski space, i.e. a space endowed with a (in general non-diagonal) metric
tensor, whose coefficients do depend on a set of non-metrical coodinates. This
is the first of a series of papers devoted to the investigation of the Killing
symmetries of generalized Minkowski spaces. In particular, we discuss here the
infinitesimal-algebraic structure of the space-time rotations in such spaces.
It is shown that the maximal Killing group of these spaces is the direct
product of a generalized Lorentz group and a generalized translation group. We
derive the explicit form of the generators of the generalized Lorentz group in
the self-representation and their related, generalized Lorentz algebra. The
results obtained are specialized to the case of a 4-dimensional, ''deformed''
Minkowski space , i.e. a pseudoeuclidean space with metric
coefficients depending on energy.Comment: 35 pages. Slightly improved version with respect to the published one
(some misprints corrected, Ref.s added, Eq.s revised, comments made
Singular integrals along variable codimension one subspaces
This article deals with maximal operators on formed by taking
arbitrary rotations of tensor products of a -dimensional H\"ormander-Mihlin
multiplier with the identity in coordinates, in the particular
codimension 1 case . These maximal operators are naturally connected to
differentiation problems and maximally modulated singular integrals such as
Sj\"olin's generalization of Carleson's maximal operator. Our main result, a
weak-type -estimate on band-limited functions, leads to
several corollaries. The first is a sharp estimate for the
maximal operator restricted to a finite set of rotations in terms of the
cardinality of the finite set. The second is a version of the Carleson-Sj\"olin
theorem. In addition, we obtain that functions in the Besov space
, , may be recovered from their
averages along a measurable choice of codimension subspaces, a form of
Zygmund's conjecture in general dimension .Comment: 49 pages, 3 figures. Submitted for publicatio
Platonic solids generate their four-dimensional analogues
This paper shows how regular convex 4-polytopes â the analogues of the Platonic solids in four dimensions â can be constructed from three-dimensional considerations concerning the Platonic solids alone. Via the CartanâDieudonneÂŽ theorem, the reflective symmetries of the Platonic solids generate rotations. In a Clifford algebra framework, the space of spinors generating such threedimensional rotations has a natural four-dimensional Euclidean structure. The spinors arising from the Platonic solids can thus in turn be interpreted as vertices in four-dimensional space, giving a simple construction of the four-dimensional polytopes 16-cell, 24-cell, the F4 root system and the 600-cell. In particular, these polytopes have âmysteriousâ symmetries, that are almost trivial when seen from the three-dimensional spinorial point of view. In fact, all these induced polytopes are also known to be root systems and thus generate rank-4 Coxeter groups, which can be shown to be a general property of the spinor construction. These considerations thus also apply to other root systems such as A1+I2(n) which induces I2(n)+I2(n), explaining the existence of the grand antiprism and the snub 24-cell, as well as their symmetries. These results are discussed in the wider mathematical context of Arnoldâs trinities and the McKay correspondence. These results are thus a novel link between the geometries of three and four dimensions, with interesting potential applications on both sides of the correspondence, to real three-dimensional systems with polyhedral symmetries such as (quasi)crystals and viruses, as well as four-dimensional geometries arising for instance in Grand Unified Theories and string and M-theory
The structure of N=2 supersymmetric nonlinear sigma models in AdS_4
We present a detailed study of the most general N=2 supersymmetric sigma
models in four-dimensional anti-de Sitter space AdS_4 formulated in terms of
N=1 chiral superfields. The target space is demonstrated to be a non-compact
hyperkahler manifold restricted to possess a special Killing vector field which
generates an SO(2) group of rotations on the two-sphere of complex structures
and necessarily leaves one of them invariant. All hyperkahler cones, that is
the target spaces of N=2 superconformal sigma models, prove to possess such a
vector field that belongs to the Lie algebra of an isometry group SU(2) acting
by rotations on the complex structures. A unique property of the N=2 sigma
models constructed is that the algebra of OSp(2|4) transformations closes off
the mass shell. We uncover the underlying N=2 superfield formulation for the
N=2 sigma models constructed and compute the associated N=2 supercurrent.
We give a special analysis of the most general systems of self-interacting
N=2 tensor multiplets in AdS_4 and their dual sigma models realized in terms of
N=1 chiral multiplets. We also briefly discuss the relationship between our
results on N=2 supersymmetric sigma models formulated in the N=1 AdS superspace
and the off-shell sigma models constructed in the N=2 AdS superspace in
arXiv:0807.3368.Comment: 84 pages; v2: typos corrected, version published in JHE
Self-dual supersymmetric nonlinear sigma models
In four-dimensional N=1 Minkowski superspace, general nonlinear sigma models
with four-dimensional target spaces may be realised in term of CCL (chiral and
complex linear) dynamical variables which consist of a chiral scalar, a complex
linear scalar and their conjugate superfields. Here we introduce CCL sigma
models that are invariant under U(1) "duality rotations" exchanging the
dynamical variables and their equations of motion. The Lagrangians of such
sigma models prove to obey a partial differential equation that is analogous to
the self-duality equation obeyed by U(1) duality invariant models for nonlinear
electrodynamics. These sigma models are self-dual under a Legendre
transformation that simultaneously dualises (i) the chiral multiplet into a
complex linear one; and (ii) the complex linear multiplet into a chiral one.
Any CCL sigma model possesses a dual formulation given in terms of two chiral
multiplets. The U(1) duality invariance of the CCL sigma model proves to be
equivalent, in the dual chiral formulation, to a manifest U(1) invariance
rotating the two chiral scalars. Since the target space has a holomorphic
Killing vector, the sigma model possesses a third formulation realised in terms
of a chiral multiplet and a tensor multiplet.
The family of U(1) duality invariant CCL sigma models includes a subset of
N=2 supersymmetric theories. Their target spaces are hyper Kahler manifolds
with a non-zero Killing vector field. In the case that the Killing vector field
is triholomorphic, the sigma model admits a dual formulation in terms of a
self-interacting off-shell N=2 tensor multiplet.
We also identify a subset of CCL sigma models which are in a one-to-one
correspondence with the U(1) duality invariant models for nonlinear
electrodynamics. The target space isometry group for these sigma models
contains a subgroup U(1) x U(1).Comment: 22 page
Load displacement behavior of the human Lumbo-sacral joint
The three-dimensional load displacement behavior of nine fresh adult L5-S1 spine motion segments was studied. Static test forces up to 160 N in anterior, posterior, and lateral shear, test forces up to 320 N in compression, and test moments up to 15.7 Nm in flexion, extension, lateral bending, and torsion were used. The six displacements of the center of the inferior L5 endplate were measured 15 and 60 s after the load was applied. Specimens were then retested after posterior element excision. The results show that at the maximum test force, intact specimen mean (sd) displacements ranged from 1.65 mm (0.63 mm) in lateral shear to 2.21 mm (0.87 mm) in posterior shear. Posterior element excision resulted in an average 1.66-fold increase in shear translations. At the maximum moment, rotations ranged from 3.38° (1.03°) in torsion to 7.19° (1.77°) in flexion. Posterior element excision resulted in an average 2.09-fold increase in bending rotations and a 2.74-fold increase in the average torsional rotation. In general, these L5-S1 joints were stiffer than more cranial lumbar segments in flexion, extension, and lateral bending and were less stiff in torsion tests.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50380/1/1100050404_ftp.pd
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