1,094 research outputs found
On the Chiral WZNW Phase Space, Exchange r-Matrices and Poisson-Lie Groupoids
This is a review of recent work on the chiral extensions of the WZNW phase
space describing both the extensions based on fields with generic monodromy as
well as those using Bloch waves with diagonal monodromy. The symplectic form on
the extended phase space is inverted in both cases and the chiral WZNW fields
are found to satisfy quadratic Poisson bracket relations characterized by
monodromy dependent exchange r-matrices. Explicit expressions for the exchange
r-matrices in terms of the arbitrary monodromy dependent 2-form appearing in
the chiral WZNW symplectic form are given. The exchange r-matrices in the
general case are shown to satisfy a new dynamical generalization of the
classical modified Yang-Baxter (YB) equation and Poisson-Lie (PL) groupoids are
constructed that encode this equation analogously as PL groups encode the
classical YB equation. For an arbitrary simple Lie group , exchange
r-matrices are exhibited that are in one-to-one correspondence with the
possible PL structures on and admit them as PL symmetries.Comment: Based on a lecture by L.F. at the Seminaire de Mathematiques
Superieures, Montreal, 1999; LaTeX, 21 page
Coadjoint orbits of the Virasoro algebra and the global Liouville equation
The classification of the coadjoint orbits of the Virasoro algebra is
reviewed and is then applied to analyze the so-called global Liouville
equation. The review is self-contained, elementary and is tailor-made for the
application. It is well-known that the Liouville equation for a smooth, real
field under periodic boundary condition is a reduction of the SL(2,R)
WZNW model on the cylinder, where the WZNW field g in SL(2,R) is restricted to
be Gauss decomposable. If one drops this restriction, the Hamiltonian reduction
yields, for the field where is a constant,
what we call the global Liouville equation. Corresponding to the winding number
of the SL(2,R) WZNW model there is a topological invariant in the reduced
theory, given by the number of zeros of Q over a period. By the substitution
, the Liouville theory for a smooth is recovered in
the trivial topological sector. The nontrivial topological sectors can be
viewed as singular sectors of the Liouville theory that contain blowing-up
solutions in terms of . Since the global Liouville equation is
conformally invariant, its solutions can be described by explicitly listing
those solutions for which the stress-energy tensor belongs to a set of
representatives of the Virasoro coadjoint orbits chosen by convention. This
direct method permits to study the `coadjoint orbit content' of the topological
sectors as well as the behaviour of the energy in the sectors. The analysis
confirms that the trivial topological sector contains special orbits with
hyperbolic monodromy and shows that the energy is bounded from below in this
sector only.Comment: Plain TEX, 48 pages, final version to appear in IJMP
The Chiral WZNW Phase Space and its Poisson-Lie Groupoid
The precise relationship between the arbitrary monodromy dependent 2-form
appearing in the chiral WZNW symplectic form and the `exchange r-matrix' that
governs the corresponding Poisson brackets is established. Generalizing earlier
results related to diagonal monodromy, the exchange r-matrices are shown to
satisfy a new dynamical generalization of the classical modified Yang-Baxter
equation, which is found to admit an interpretation in terms of (new)
Poisson-Lie groupoids. Dynamical exchange r-matrices for which right
multiplication yields a classical or a Poisson-Lie symmetry on the chiral WZNW
phase space are presented explicitly.Comment: 13 pages, LaTeX, minor typos correcte
Building simulated queries for known-item topics: an analysis using six european languages
There has been increased interest in the use of simulated queries for evaluation and estimation purposes in Information Retrieval. However, there are still many unaddressed issues regarding their usage and impact on evaluation because their quality, in terms of retrieval performance, is unlike real queries. In this paper, we focus on methods for building simulated known-item topics and explore their quality against real known-item topics. Using existing generation models as our starting point, we explore factors which may influence the generation of the known-item topic. Informed by this detailed analysis (on six European languages) we propose a model with improved document and term selection properties, showing that simulated known-item topics can be generated that are comparable to real known-item topics. This is a significant step towards validating the potential usefulness of simulated queries: for evaluation purposes, and because building models of querying behavior provides a deeper insight into the querying process so that better retrieval mechanisms can be developed to support the user
Quantum corrections of Abelian Duality Transformations
A modification of the Abelian Duality transformations is proposed
guaranteeing that a (not necessarily conformally invariant) -model be
quantum equivalent (at least up to two loops in perturbation theory) to its
dual. This requires a somewhat non standard perturbative treatment of the {\sl
dual} -model. Explicit formulae of the modified duality transformation
are presented for a special class of block diagonal purely metric
-models.Comment: Latex 11 pages; remarks on a free model and references adde
Dynamical r-matrices and the chiral WZNW phase space
The dynamical generalization of the classical Yang-Baxter equation that
governs the possible Poisson structures on the space of chiral WZNW fields with
generic monodromy is reviewed. It is explained that for particular choices of
the chiral WZNW Poisson brackets this equation reduces to the CDYB equation
recently studied by Etingof--Varchenko and others. Interesting dynamical
r-matrices are obtained for generic monodromy as well as by imposing Dirac
constraints on the monodromy.Comment: Talk given at XXIII International Colloquium on Group Theoretical
Methods in Physics, July 31 - August 5, 2000, Dubna, Russia. LaTeX, 9 page
Quantum sl_n Toda field theories
We quantize Toda field theories in a periodic lattice. We find the
quantum exchange algebra in the diagonal monodromy (Bloch wave) basis in the
case of the defining representation. In the case we extend the analysis
also to the second fundamental representation. We clarify, in particular, the
relation of Jimbo and Rosso's quantum matrix with the quantum matrix in
the Bloch wave basis.Comment: 19 pages, SISSA-ISAS 110/92/E
Dusty Cometary Globules in W5
We report the discovery of four dusty cometary tails around low mass stars in
two young clusters belonging to the W5 star forming region. Fits to the
observed emission profiles from 24 micron observations with the Spitzer Space
Telescope give tail lifetimes < 30 Myr, but more likely < 5 Myr. This result
suggests that the cometary phase is a short lived phenomenon, occurring after
photoevaporation by a nearby O star has removed gas from the outer disk of a
young low mass star (see also Balog et al. 2006; Balog et al. 2008).Comment: 11 pages, 3 figures. Accepted for publication to ApJ Letter
Scaling function in AdS/CFT from the O(6) sigma model
Asymptotic behavior of the anomalous dimensions of Wilson operators with high
spin and twist is governed in planar N=4 SYM theory by the scaling function
which coincides at strong coupling with the energy density of a two-dimensional
bosonic O(6) sigma model. We calculate this function by combining the two-loop
correction to the energy density for the O(n) model with two-loop correction to
the mass gap determined by the all-loop Bethe ansatz in N=4 SYM theory. The
result is in agreement with the prediction coming from the thermodynamical
limit of the quantum string Bethe ansatz equations, but disagrees with the
two-loop stringy corrections to the folded spinning string solution.Comment: 25 pages, 2 figure
Chiral extensions of the WZNW phase space, Poisson-Lie symmetries and groupoids
The chiral WZNW symplectic form is inverted in the general case. Thereby a precise relationship between the arbitrary monodromy dependent 2-form appearing in and the exchange r-matrix that governs the Poisson brackets of the group valued chiral fields is established. The exchange r-matrices are shown to satisfy a new dynamical generalization of the classical modified Yang-Baxter (YB) equation and Poisson-Lie (PL) groupoids are constructed that encode this equation analogously as PL groups encode the classical YB equation. For an arbitrary simple Lie group G, exchange r-matrices are found that are in one-to-one correspondence with the possible PL structures on G and admit them as PL symmetries
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