21 research outputs found
Poisson-Lie T-duality and loop groups of Drinfeld doubles
A duality invariant first order action is constructed on the loop group of a Drinfeld double. It gives at the same time the description of both of the pair of \sigma-models related by Poisson-Lie T-duality. Remarkably, the action contains a WZW-term on the Drinfeld double not only for conformally invariant \si-models. The resulting actions of the models from the dual pair differ just by a total derivative corresponding to an ambiguity in specifying a two-form whose exterior derivative is the WZW three-form. This total derivative is nothing but the Semenov-Tian-Shansky symplectic form on the Drinfeld double and it gives directly a generating function of the canonical transformation relating the \si-models from the dual pair
Affine Poisson Groups and WZW Model
We give a detailed description of a dynamical system which enjoys a Poisson-Lie symmetry with two non-isomorphic dual groups. The system is obtained by taking the q → ∞ limit of the q-deformed WZW model and the understanding of its symmetry structure results in uncovering an interesting duality of its exchange relations
Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models II: Nondiagonal metrics and dilaton puzzle
We look for 3-dimensional Poisson-Lie dualizable sigma models that satisfy
the vanishing beta-function equations with constant dilaton field. Using the
Poisson-Lie T-plurality we then construct 3-dimensional sigma models that
correspond to various decompositions of Drinfeld double. Models with nontrivial
dilaton field may appear. It turns out that for ``traceless'' dual algebras
they satisfy the vanishing beta-function equations as well.
In certain cases the dilaton cannot be defined in some of the dual models. We
provide an explanation why this happens and give criteria predicting when it
happens.Comment: 24 pages, the published version; changes compared to v1: typos
corrected, conclusions extended, added reference
On Non-Abelian Duality in Sigma Models
A method for implementing non-Abelian duality on string backgrounds is given.
It is shown that a direct generalisation of the familiar Abelian duality
induces an extra local symmetry in the gauge invariant theory. The non-Abelian
isometry group is shown to be enlarged to a non-semi-simple group. However,
upon eliminating the gauge fields to obtain the dual theory the new algebra
does not close. Therefore the gauge fixing procedure becomes problematic. The
new method proposed here avoids these issues and leads to a dual theory in the
proper sense of duality.Comment: 8 pages, Latex fil
Dual branes in topological sigma models over Lie groups. BF-theory and non-factorizable Lie bialgebras
We complete the study of the Poisson-Sigma model over Poisson-Lie groups.
Firstly, we solve the models with targets and (the dual group of the
Poisson-Lie group ) corresponding to a triangular -matrix and show that
the model over is always equivalent to BF-theory. Then, given an
arbitrary -matrix, we address the problem of finding D-branes preserving the
duality between the models. We identify a broad class of dual branes which are
subgroups of and , but not necessarily Poisson-Lie subgroups. In
particular, they are not coisotropic submanifolds in the general case and what
is more, we show that by means of duality transformations one can go from
coisotropic to non-coisotropic branes. This fact makes clear that
non-coisotropic branes are natural boundary conditions for the Poisson-Sigma
model.Comment: 24 pages; JHEP style; Final versio
Worldsheet boundary conditions in Poisson-Lie T-duality
We apply canonical Poisson-Lie T-duality transformations to bosonic open
string worldsheet boundary conditions, showing that the form of these
conditions is invariant at the classical level, and therefore they are
compatible with Poisson-Lie T-duality. In particular the conditions for
conformal invariance are automatically preserved, rendering also the dual model
conformal. The boundary conditions are defined in terms of a gluing matrix
which encodes the properties of D-branes, and we derive the duality map for
this matrix. We demonstrate explicitly the implications of this map for
D-branes in two non-Abelian Drinfel'd doubles.Comment: 20 pages, Latex; v2: typos and wording corrected, references added;
v3: three-dimensional example added, reference added, discussion clarified,
published versio
Non-Abelian Duality and Canonical Transformations
We construct explicit canonical transformations producing non-abelian duals
in principal chiral models with arbitrary group G. Some comments concerning the
extension to more general -models, like WZW models, are given.Comment: 9 pags, latex fil
Anti-field Formalism and Non-Abelian Duality
The act of implementing non-Abelian duality in two dimensional sigma models
results unavoidably in an additional reducible symmetry. The Batalin-Vilkovisky
formalism is employed to handle this new symmetry. Valuable lessons are learnt
here with respect to non-Abelian duality. We emphasise, in particular, the
effects of the ghost sector corresponding to this symmetry on non-Abelian
duality.Comment: 13 pages, LaTeX2