532 research outputs found

### The SU(n)_1 WZW Models: Spinon Decomposition and Yangian Structure

We present a `spinon formulation' of the $SU(n)_1$ Wess-Zumino-Witten models.
Central to this approach are a set of massless quasi-particles, called
`spinons', which transform in the representation ${\bf \bar{n}}$ of $su(n)$ and
carry fractional statistics of angle $\theta = \pi/n$. Multi-spinon states are
grouped into irreducible representations of the yangian $Y(sl_n)$. We give
explicit results for the $su(n)$ content of these yangian representations and
present $N$-spinon cuts of the WZW character formulas. As a by-product, we
obtain closed expressions for characters of the $su(n)$ Haldane-Shastry spin
chains.Comment: 38 pages, LaTeX, no figure

### The deformed Virasoro algebra at roots of unity

We discuss some aspects of the representation theory of the deformed Virasoro
algebra \virpq. In particular, we give a proof of the formula for the Kac
determinant and then determine the center of \virpq for $q$ a primitive N-th
root of unity. We derive explicit expressions for the generators of the center
in the limit $t=qp^{-1}\to \infty$ and elucidate the connection to the
Hall-Littlewood symmetric functions. Furthermore, we argue that for
q=\sqrtN{1} the algebra describes `Gentile statistics' of order $N-1$, i.e.,
a situation in which at most $N-1$ particles can occupy the same state.Comment: 51 pages, TeX (with amssym.def

### On deformed W-algebras and quantum affine algebras

We discuss some aspects of the deformed W-algebras W_{q,t}[g]. In particular,
we derive an explicit formula for the Kac determinant, and discuss the center
when t^2 is a primitive k-th root of unity. The relation of the structure of
W_{q,t}[g] to the representation ring of the quantum affine algebra U_q(\hat
g), as discovered recently by Frenkel and Reshetikhin, is further elucidated in
some examples.Comment: 40 pages, plain TeX with amssym.def, improved referencin

### T-duality for principal torus bundles

In this paper we study T-duality for principal torus bundles with H-flux. We
identify a subset of fluxes which are T-dualizable, and compute both the dual
torus bundle as well as the dual H-flux. We briefly discuss the generalized
Gysin sequence behind this construction and provide examples both of non
T-dualizable and of T-dualizable H-fluxes.Comment: 9 pages, typos removed and minor corrections mad

### Graded parafermions: standard and quasi-particle bases

Two bases of states are presented for modules of the graded parafermionic
conformal field theory associated to the coset \osp(1,2)_k/\uh(1). The first
one is formulated in terms of the two fundamental (i.e., lowest dimensional)
parafermionic modes. In that basis, one can identify the completely reducible
representations, i.e., those whose modules contain an infinite number of
singular vectors; the explicit form of these vectors is also given.
The second basis is a quasi-particle basis, determined in terms of a modified
version of the \ZZ_{2k} exclusion principle. A novel feature of this model is
that none of its bases are fully ordered and this reflects a hidden structural
$\Z_3$ exclusion principle.Comment: Harvmac 24 p; minor corrections in eqs 5.2 and 5.

### Distribution of satellite galaxies in high redshift groups

We use galaxy groups at redshifts between 0.4 and 1.0 selected from the Great
Observatories Origins Deep Survey (GOODS) to study the color-morphological
properties of satellite galaxies, and investigate possible alignment between
the distribution of the satellites and the orientation of their central galaxy.
We confirm the bimodal color and morphological type distribution for satellite
galaxies at this redshift range: the red and blue classes corresponds to the
early and late morphological types respectively, and the early-type satellites
are on average brighter than the late-type ones. Furthermore, there is a {\it
morphological conformity} between the central and satellite galaxies: the
fraction of early-type satellites in groups with an early-type central is
higher than those with a late-type central galaxy. This effect is stronger at
smaller separations from the central galaxy. We find a marginally significant
signal of alignment between the major axis of the early-type central galaxy and
its satellite system, while for the late-type centrals no significant alignment
signal is found. We discuss the alignment signal in the context of shape
evolution of groups.Comment: 7 pages, 7 figures, accepted by Ap

### Presentations of Wess-Zumino-Witten Fusion Rings

The fusion rings of Wess-Zumino-Witten models are re-examined. Attention is
drawn to the difference between fusion rings over Z (which are often of greater
importance in applications) and fusion algebras over C. Complete proofs are
given characterising the fusion algebras (over C) of the SU(r+1) and Sp(2r)
models in terms of the fusion potentials, and it is shown that the analagous
potentials cannot describe the fusion algebras of the other models. This
explains why no other representation-theoretic fusion potentials have been
found.
Instead, explicit generators are then constructed for general WZW fusion
rings (over Z). The Jacobi-Trudy identity and its Sp(2r) analogue are used to
derive the known fusion potentials. This formalism is then extended to the WZW
models over the spin groups of odd rank, and explicit presentations of the
corresponding fusion rings are given. The analogues of the Jacobi-Trudy
identity for the spinor representations (for all ranks) are derived for this
purpose, and may be of independent interest.Comment: 32 pages, 3 figures, added references, minor additions to text. To be
published in Rev. Math. Phy

### Non-abelian quantum Hall states - exclusion statistics, K-matrices and duality

We study excitations in edge theories for non-abelian quantum Hall states,
focussing on the spin polarized states proposed by Read and Rezayi and on the
spin singlet states proposed by two of the authors. By studying the exclusion
statistics properties of edge-electrons and edge-quasiholes, we arrive at a
novel K-matrix structure. Interestingly, the duality between the electron and
quasihole sectors links the pseudoparticles that are characteristic for
non-abelian statistics with composite particles that are associated to the
`pairing physics' of the non-abelian quantum Hall states.Comment: LaTeX2e, 40 page

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