307 research outputs found
Generating-function method for tensor products
This is the first of two articles devoted to a exposition of the
generating-function method for computing fusion rules in affine Lie algebras.
The present paper is entirely devoted to the study of the tensor-product
(infinite-level) limit of fusions rules.
We start by reviewing Sharp's character method. An alternative approach to
the construction of tensor-product generating functions is then presented which
overcomes most of the technical difficulties associated with the character
method. It is based on the reformulation of the problem of calculating tensor
products in terms of the solution of a set of linear and homogeneous
Diophantine equations whose elementary solutions represent ``elementary
couplings''. Grobner bases provide a tool for generating the complete set of
relations between elementary couplings and, most importantly, as an algorithm
for specifying a complete, compatible set of ``forbidden couplings''.Comment: Harvmac (b mode : 39 p) and Pictex; this is a substantially reduced
version of hep-th/9811113 (with new title); to appear in J. Math. Phy
Generating-function method for fusion rules
This is the second of two articles devoted to an exposition of the
generating-function method for computing fusion rules in affine Lie algebras.
The present paper focuses on fusion rules, using the machinery developed for
tensor products in the companion article. Although the Kac-Walton algorithm
provides a method for constructing a fusion generating function from the
corresponding tensor-product generating function, we describe a more powerful
approach which starts by first defining the set of fusion elementary couplings
from a natural extension of the set of tensor-product elementary couplings. A
set of inequalities involving the level are derived from this set using Farkas'
lemma. These inequalities, taken in conjunction with the inequalities defining
the tensor products, define what we call the fusion basis. Given this basis,
the machinery of our previous paper may be applied to construct the fusion
generating function. New generating functions for sp(4) and su(4), together
with a closed form expression for their threshold levels are presented.Comment: Harvmac (b mode : 47 p) and Pictex; to appear in J. Math. Phy
The optical companion to the binary millisecond pulsar J1824-2452H in the globular cluster M28
We report on the optical identification of the companion star to the
eclipsing millisecond pulsar PSR J1824-2452H in the galactic globular cluster
M28 (NGC 6626). This star is at only 0.2" from the nominal position of the
pulsar and it shows optical variability (~ 0.25 mag) that nicely correlates
with the pulsar orbital period. It is located on the blue side of the cluster
main sequence, ~1.5 mag fainter than the turn-off point. The observed light
curve shows two distinct and asymmetric minima, suggesting that the companion
star is suffering tidal distortion from the pulsar. This discovery increases
the number of non-degenerate MSP companions optically identified so far in
globular clusters (4 out of 7), suggesting that these systems could be a common
outcome of the pulsar recycling process, at least in dense environments where
they can be originated by exchange interactions.Comment: accepted for publication on ApJ, 17 pages, 5 figure
Constraining the luminosity function parameters and population size of radio pulsars in globular clusters
Studies of the Galactic population of radio pulsars have shown that their
luminosity distribution appears to be log-normal in form. We investigate some
of the consequences that occur when one applies this functional form to
populations of pulsars in globular clusters. We use Bayesian methods to explore
constraints on the mean and standard deviation of the luminosity function, as
well as the total number of pulsars, given an observed sample of pulsars down
to some limiting flux density, accounting for measurements of flux densities of
individual pulsars as well as diffuse emission from the direction of the
cluster. We apply our analysis to Terzan 5, 47 Tucanae and M 28, and
demonstrate, under reasonable assumptions, that the number of potentially
observable pulsars should be within 95% credible intervals of
, and , respectively.
Beaming considerations would increase the true population size by approximately
a factor of two. Using non-informative priors, however, the constraints are not
tight due to the paucity and quality of flux density measurements. Future
cluster pulsar discoveries and improved flux density measurements would allow
this method to be used to more accurately constrain the luminosity function,
and to compare the luminosity function between different clusters.Comment: 9 pages, 4 figures, Accepted for publication in MNRA
Berenstein-Zelevinsky triangles, elementary couplings and fusion rules
We present a general scheme for describing su(N)_k fusion rules in terms of
elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling
is characterized by its corresponding tensor product coupling (i.e. its
Berenstein-Zelevinsky triangle) and the threshold level at which it first
appears. We show that a closed expression for this threshold level is encoded
in the Berenstein-Zelevinsky triangle and an explicit method to calculate it is
presented. In this way a complete solution of su(4)_k fusion rules is obtained.Comment: 14 page
Extended radio emission in the galaxy cluster MS 0735.6+7421 detected with the Karl G. Jansky Very Large Array
MS 0735.6+7421 () is a massive cool core galaxy cluster hosting
one of the most powerful active galactic nuclei (AGN) outbursts known. The
radio jets of the AGN have carved out an unusually large pair of X-ray
cavities, each reaching a diameter of kpc. This makes MS 0735.6+7421 a
unique case to investigate active galactic nuclei feedback processes, as well
as other cluster astrophysics at radio wavelengths. We present new
low-radio-frequency observations of MS 0735.6+7421 taken with the Karl G.
Jansky Very Large Array (VLA): 5 hours of P-band ( MHz) and 5 hours of
L-band ( GHz) observations, both in C configuration. Our VLA P-band
( MHz) observations reveal the presence of a new diffuse radio
component reaching a scale of kpc in the direction of the jets and
of kpc in the direction perpendicular to the jets. This component
is centered on the cluster core and has a radio power scaled at GHz of
WHz. Its properties are
consistent with those expected from a radio mini-halo as seen in other massive
cool core clusters, although it may also be associated with radio plasma that
has diffused out of the X-ray cavities. Observations at higher spatial
resolution are needed to fully characterize the properties and nature of this
component. We also suggest that if radio mini-halos originate from jetted
activity, we may be witnessing the early stages of this process.Comment: 11 pages, 7 figures, submitted to MNRA
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