339 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
Fusion multiplicities as polytope volumes: N-point and higher-genus su(2) fusion
We present the first polytope volume formulas for the multiplicities of
affine fusion, the fusion in Wess-Zumino-Witten conformal field theories, for
example. Thus, we characterise fusion multiplicities as discretised volumes of
certain convex polytopes, and write them explicitly as multiple sums measuring
those volumes. We focus on su(2), but discuss higher-point (N>3) and
higher-genus fusion in a general way. The method follows that of our previous
work on tensor product multiplicities, and so is based on the concepts of
generalised Berenstein-Zelevinsky diagrams, and virtual couplings. As a
by-product, we also determine necessary and sufficient conditions for
non-vanishing higher-point fusion multiplicities. In the limit of large level,
these inequalities reduce to very simple non-vanishing conditions for the
corresponding tensor product multiplicities. Finally, we find the minimum level
at which the higher-point fusion and tensor product multiplicities coincide.Comment: 14 pages, LaTeX, version to be publishe
On the level-dependence of Wess-Zumino-Witten three-point functions
Three-point functions of Wess-Zumino-Witten models are investigated. In
particular, we study the level-dependence of three-point functions in the
models based on algebras and . We find a correspondence with
Berenstein-Zelevinsky triangles. Using previous work connecting those triangles
to the fusion multiplicities, and the Gepner-Witten depth rule, we explain how
to construct the full three-point functions. We show how their level-dependence
is similar to that of the related fusion multiplicity. For example, the concept
of threshold level plays a prominent role, as it does for fusion.Comment: 24 pages, no figure
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
Teaching, research and the Canadian professoriate : findings from the 2018 APIKS survey
This paper presents the Canadian findings from the 2018 APIKS study focusing on the
teaching-research nexus. The online, bilingual survey was administered to full-time professors at 64
provincially-funded universities in Canada between October 2017 and June 2018 (n=2968). Findings
suggest the majority of full-time, tenure-steam professors prefer both teaching and research and are
engaged in both throughout the academic year. These findings are considered in light of broader
changes in Canadian higher education including enrolment expansion, the increasing valorization of
research, the development of new categories of academic labour, and the growth in precarious contract
employment
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
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
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