226 research outputs found
Classical solution of a sigma-model in curved background
We have solved a sigma-model in curved background using the fact that the
Poisson-Lie T-duality can transform the curved background into the flat one.
For finding solution of the flat model we have used transformation of
coordinates that makes the metric constant. The T-duality transform was then
explicitly performed.Comment: 7 page
Dressing cosets revisited
We present an alternative algebraic derivation of the dual pair of nonlinear
-models based on the 'dressing cosets' extension of the Poisson-Lie
-duality \cite{KS1}. Then we generalize the result to dual pairs of
Lagrangians not considered in \cite{KS1}. Our generalization turns out to
incorporate the dualisable models constructed by Sfetsos in \cite{Sfet1}.Comment: 24 page
D-branes in the Euclidean and T-duality
We show that D-branes in the Euclidean can be naturally associated to
the maximally isotropic subgroups of the Lu-Weinstein double of SU(2). This
picture makes very transparent the residual loop group symmetry of the D-brane
configurations and gives also immediately the D-branes shapes and the
-model boundary conditions in the de Sitter T-dual of the
WZW model.Comment: 29 pages, LaTeX, references adde
Poisson-Lie T-plurality as canonical transformation
We generalize the prescription realizing classical Poisson-Lie T-duality as
canonical transformation to Poisson-Lie T-plurality. The key ingredient is the
transformation of left-invariant fields under Poisson-Lie T-plurality. Explicit
formulae realizing canonical transformation are presented and the preservation
of canonical Poisson brackets and Hamiltonian density is shown.Comment: 11 pages. Details of calculations added, version accepted for
publicatio
Open Strings and D-branes in WZNW model
An abundance of the Poisson-Lie symmetries of the WZNW models is uncovered.
They give rise, via the Poisson-Lie -duality, to a rich structure of the
dual pairs of -branes configurations in group manifolds. The -branes are
characterized by their shapes and certain two-forms living on them. The WZNW
path integral for the interacting -branes diagrams is unambiguously defined
if the two-form on the -brane and the WZNW three-form on the group form an
integer-valued cocycle in the relative singular cohomology of the group
manifold with respect to its -brane submanifold. An example of the
WZNW model is studied in some detail.Comment: 28 pages, LaTe
On moment maps associated to a twisted Heisenberg double
We review the concept of the (anomalous) Poisson-Lie symmetry in a way that
emphasises the notion of Poisson-Lie Hamiltonian. The language that we develop
turns out to be very useful for several applications: we prove that the left
and the right actions of a group on its twisted Heisenberg double
realize the (anomalous) Poisson-Lie symmetries and we explain in a
very transparent way the concept of the Poisson-Lie subsymmetry and that of
Poisson-Lie symplectic reduction. Under some additional conditions, we
construct also a non-anomalous moment map corresponding to a sort of
quasi-adjoint action of on . The absence of the anomaly of this
"quasi-adjoint" moment map permits to perform the gauging of deformed WZW
models.Comment: 52 pages, LaTeX, introduction substantially enlarged, several
explanatory remarks added, final published versio
Dressing Cosets
The account of the Poisson-Lie T-duality is presented for the case when the
action of the duality group on a target is not free. At the same time a
generalization of the picture is given when the duality group does not even act
on \si-model targets but only on their phase spaces. The outcome is a huge
class of dualizable targets generically having no local isometries or
Poisson-Lie symmetries whatsoever.Comment: 11 pages, LaTe
On supermatrix models, Poisson geometry and noncommutative supersymmetric gauge theories
We construct a new supermatrix model which represents a manifestly
supersymmetric noncommutative regularisation of the
supersymmetric Schwinger model on the supersphere. Our construction is much
simpler than those already existing in the literature and it was found by using
Poisson geometry in a substantial way.Comment: 29 pages, we enlarge Section 3.3 by adding a comparison with older
results on the subject of the component expansion
Quasitriangular chiral WZW model in a nutshell
We give the bare-bone description of the quasitriangular chiral WZW model for
the particular choice of the Lu-Weinstein-Soibelman Drinfeld double of the
affine Kac-Moody group. The symplectic structure of the model and its
Poisson-Lie symmetry are completely characterized by two -matrices with
spectral parameter. One of them is ordinary and trigonometric and characterizes
the -current algebra. The other is dynamical and elliptic (in fact Felder's
one) and characterizes the braiding of -primary fields.Comment: 8 pages, LaTeX, to appear in the Proceedings of the Yokohama meeting
on String theory and noncommutative geometry (March 2001
Poisson-Lie T-duality
A description of dual non-Abelian duality is given, based on the notion of
the Drinfeld double. The presentation basically follows the original paper
\cite{KS2}, written in collaboration with P. \v Severa, but here the emphasis
is put on the algebraic rather than the geometric aspect of the construction
and a concrete example of the Borelian double is worked out in detail.Comment: 11 pages, LaTeX, Lecture given at Trieste conference on S-duality and
mirror symmetry, June 1995, (signs in Eqs. (10,11) corrected, 1 reference
added
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