4,792 research outputs found
Global analysis by hidden symmetry
Hidden symmetry of a G'-space X is defined by an extension of the G'-action
on X to that of a group G containing G' as a subgroup. In this setting, we
study the relationship between the three objects:
(A) global analysis on X by using representations of G (hidden symmetry);
(B) global analysis on X by using representations of G';
(C) branching laws of representations of G when restricted to the subgroup
G'.
We explain a trick which transfers results for finite-dimensional
representations in the compact setting to those for infinite-dimensional
representations in the noncompact setting when is -spherical.
Applications to branching problems of unitary representations, and to spectral
analysis on pseudo-Riemannian locally symmetric spaces are also discussed.Comment: Special volume in honor of Roger Howe on the occasion of his 70th
birthda
Testing the Master Constraint Programme for Loop Quantum Gravity III. SL(2,R) Models
This is the third paper in our series of five in which we test the Master
Constraint Programme for solving the Hamiltonian constraint in Loop Quantum
Gravity. In this work we analyze models which, despite the fact that the phase
space is finite dimensional, are much more complicated than in the second
paper: These are systems with an SL(2,\Rl) gauge symmetry and the
complications arise because non -- compact semisimple Lie groups are not
amenable (have no finite translation invariant measure). This leads to severe
obstacles in the refined algebraic quantization programme (group averaging) and
we see a trace of that in the fact that the spectrum of the Master Constraint
does not contain the point zero. However, the minimum of the spectrum is of
order which can be interpreted as a normal ordering constant arising
from first class constraints (while second class systems lead to normal
ordering constants). The physical Hilbert space can then be be obtained after
subtracting this normal ordering correction.Comment: 33 pages, no figure
Special functions associated to a certain fourth order differential equation
We develop a theory of "special functions" associated to a certain fourth
order differential operator on depending
on two parameters . For integers with
this operator extends to a self-adjoint operator on
with discrete spectrum. We find a closed
formula for the generating functions of the eigenfunctions, from which we
derive basic properties of the eigenfunctions such as orthogonality,
completeness, -norms, integral representations and various recurrence
relations.
This fourth order differential operator arises as the
radial part of the Casimir action in the Schr\"odinger model of the minimal
representation of the group , and our "special functions" give
-finite vectors
Universal properties of superconformal OPEs for 1/2 BPS operators in
We give a general analysis of OPEs of 1/2 BPS superfield operators for the
superconformal algebras OSp(8/4,R), PSU(2,2), F and
OSp() which underlie maximal AdS supergravity in . \\
The corresponding three-point functions can be formally factorized in a way
similar to the decomposition of a generic superconformal UIR into a product of
supersingletons. This allows for a simple derivation of branching rules for
primary superfields. The operators of protected conformal dimension which may
appear in the OPE are classified and are shown to be either 1/2 or 1/4 BPS, or
semishort. As an application, we discuss the "non-renormalization" of extremal
-point correlators.Comment: To be published in NJP Focus Issue: Supersymmetry in condensed matter
and high energy physic
Testing the Master Constraint Programme for Loop Quantum Gravity II. Finite Dimensional Systems
This is the second paper in our series of five in which we test the Master
Constraint Programme for solving the Hamiltonian constraint in Loop Quantum
Gravity. In this work we begin with the simplest examples: Finite dimensional
models with a finite number of first or second class constraints, Abelean or
non -- Abelean, with or without structure functions.Comment: 23 pages, no figure
Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring
We construct a zero-curvature Lax connection in a sub-sector of the
superstring theory on AdS(4) x CP(3) which is not described by the
OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In this sub-sector worldsheet
fermions associated to eight broken supersymmetries of the type IIA background
are physical fields. As such, the prescription for the construction of the Lax
connection based on the Z_4-automorphism of the isometry superalgebra OSp(6|4)
does not do the job. So, to construct the Lax connection we have used an
alternative method which nevertheless relies on the isometry of the target
superspace and kappa-symmetry of the Green-Schwarz superstring.Comment: 1+26 pages; v2: minor typos corrected, acknowledgements adde
Supersymmetry and Positive Energy in Classical and Quantum Two-Dimensional Dilaton Gravity
An supersymmetric version of two dimensional dilaton gravity coupled
to matter is considered. It is shown that the linear dilaton vacuum
spontaneously breaks half the supersymmetries, leaving broken a linear
combination of left and right supersymmetries which squares to time
translations. Supersymmetry suggests a spinorial expression for the ADM energy
, as found by Witten in four-dimensional general relativity. Using this
expression it is proven that is non-negative for smooth initial data
asymptotic (in both directions) to the linear dilaton vacuum, provided that the
(not necessarily supersymmetric) matter stress tensor obeys the dominant energy
condition. A {\it quantum} positive energy theorem is also proven for the
semiclassical large- equations, despite the indefiniteness of the quantum
stress tensor. For black hole spacetimes, it is shown that is bounded from
below by , where is the value of the dilaton at the
apparent horizon, provided only that the stress tensor is positive outside the
apparent horizon. This is the two-dimensional analogue of an unproven
conjecture due to Penrose. Finally, supersymmetry is used to prove positive
energy theorems for a large class of generalizations of dilaton gravity which
arise in consideration of the quantum theory.Comment: 21 page
Two-Dimensional Helioseismic Power, Phase, and Coherence Spectra of {\it Solar Dynamics Observatory} Photospheric and Chromospheric Observables
While the {\it Helioseismic and Magnetic Imager} (HMI) onboard the {\it Solar
Dynamics Observatory} (SDO) provides Doppler velocity [], continuum
intensity [], and line-depth [] observations, each of which is
sensitive to the five-minute acoustic spectrum, the {\it Atmospheric Imaging
Array} (AIA) also observes at wavelengths -- specifically the 1600 and 1700
Angstrom bands -- that are partly formed in the upper photosphere and have good
sensitivity to acoustic modes. In this article we consider the characteristics
of the spatio--temporal Fourier spectra in AIA and HMI observables for a
15-degree region around NOAA Active Region 11072. We map the
spatio--temporal-power distribution for the different observables and the HMI
Line Core [], or Continuum minus Line Depth, and the phase and coherence
functions for selected observable pairs, as a function of position and
frequency. Five-minute oscillation power in all observables is suppressed in
the sunspot and also in plage areas. Above the acoustic cut-off frequency, the
behaviour is more complicated: power in HMI is still suppressed in the
presence of surface magnetic fields, while power in HMI and the AIA bands
is suppressed in areas of surface field but enhanced in an extended area around
the active region, and power in HMI is enhanced in a narrow zone around
strong-field concentrations and suppressed in a wider surrounding area. The
relative phase of the observables, and their cross-coherence functions, are
also altered around the active region. These effects may help us to understand
the interaction of waves and magnetic fields in the different layers of the
photosphere, and will need to be taken into account in multi-wavelength local
helioseismic analysis of active regions.Comment: 18 pages, 15 figures, to be published in Solar Physic
M2-M5 blackfold funnels
We analyze the basic M2-M5 intersection in the supergravity regime using the
blackfold approach. This approach allows us to recover the 1/4-BPS self-dual
string soliton solution of Howe, Lambert and West as a three-funnel solution of
an effective fivebrane worldvolume theory in a new regime, the regime of a
large number of M2 and M5 branes. In addition, it allows us to discuss finite
temperature effects for non-extremal self-dual string soliton solutions and
wormhole solutions interpolating between stacks of M5 and anti-M5 branes. The
purpose of this paper is to exhibit these solutions and their basic properties.Comment: 19 pages, 5 figures, harvmac; typo corrected in equation (3.19
Fermion Helicity Flip Induced by Torsion Field
We show that in theories of gravitation with torsion the helicity of fermion
particles is not conserved and we calculate the probability of spin flip, which
is related to the anti-symmetric part of affine connection. Some cosmological
consequences are discussed.Comment: 6 pages, to appear in Europhysics Letter
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