313 research outputs found
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
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
Joint constraints on reionization: a framework for combining the global 21cm signal and the kinetic Sunyaev-Zel'dovich effect
Recent measurements from the CMB and from high-redshift galaxy observations have placed rough constraints on the midpoint and duration of the Epoch of Reionization. Detailed measurements of the ionization history remain elusive, although two proposed probes show great promise for this purpose: the 21cm global signal and the kinetic Sunyaev-Zel'dovich (kSZ) effect. We formally confirm the common assumption that these two probes are highly complementary, with the kSZ being more sensitive to extended ionization histories and the global signal to rapidly evolving ones. We do so by performing a Karhunen-Lo\`{e}ve (KL) transformation, which casts the data in a basis designed to emphasize the information content of each probe. We find that reconstructing the ionization history using both probes gives significantly more precise results than individual constraints, although carefully chosen, physically motivated priors play a crucial part in obtaining a bias-free reconstruction. Additionally, in the KL basis, measurements from one probe can be used to detect the presence of residual systematics in the other, providing a safeguard against systematics that would go undetected when data from each probe is analyzed in isolation. Once detected, the modes contaminated by systematics can be discarded from the data analysis to avoid biases in reconstruction
Affine su(3) and su(4) fusion multiplicities as polytope volumes
Affine su(3) and su(4) fusion multiplicities are characterised as discretised
volumes of certain convex polytopes. The volumes are measured explicitly,
resulting in multiple sum formulas. These are the first polytope-volume
formulas for higher-rank fusion multiplicities. The associated threshold levels
are also discussed. For any simple Lie algebra we derive an upper bound on the
threshold levels using a refined version of the Gepner-Witten depth rule.Comment: 16 pages, LaTe
Fermionic characters for graded parafermions
Fermionic-type character formulae are presented for charged
irreduciblemodules of the graded parafermionic conformal field theory
associated to the coset . This is obtained by counting the
weakly ordered `partitions' subject to the graded exclusion principle.
The bosonic form of the characters is also presented.Comment: 24 p. This corrects typos (present even in the published version) in
eqs (4.4), (5.23), (5.24) and (C.4
Automorphisms of the affine SU(3) fusion rules
We classify the automorphisms of the (chiral) level-k affine SU(3) fusion
rules, for any value of k, by looking for all permutations that commute with
the modular matrices S and T. This can be done by using the arithmetic of the
cyclotomic extensions where the problem is naturally posed. When k is divisible
by 3, the automorphism group (Z_2) is generated by the charge conjugation C. If
k is not divisible by 3, the automorphism group (Z_2 x Z_2) is generated by C
and the Altsch\"uler--Lacki--Zaugg automorphism. Although the combinatorial
analysis can become more involved, the techniques used here for SU(3) can be
applied to other algebras.Comment: 21 pages, plain TeX, DIAS-STP-92-4
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
New insights into the pathogenesis of glucocorticoid-induced avascular necrosis: microarray analysis of gene expression in a rat model
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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