20 research outputs found
Poisson-Lie T-Duality: the Path-Integral Derivation
We formulate Poisson-Lie T-duality in a path-integral manner that allows us
to analyze the quantum corrections. Using the path-integral, we rederive the
most general form of a Poisson-Lie dualizeable background and the generalized
Buscher transformation rules it has to satisfy.Comment: 16 pages, plain LaTeX 2e, one paragraph added to the conclusions;
this is the final version accepted by Physics Letters
Notes on noncommutative supersymmetric gauge theory on the fuzzy supersphere
In these notes we review Klimcik's construction of noncommutative gauge
theory on the fuzzy supersphere. This theory has an exact SUSY gauge symmetry
with a finite number of degrees of freedom and thus in principle it is amenable
to the methods of matrix models and Monte Carlo numerical simulations. We also
write down in this article a novel fuzzy supersymmetric scalar action on the
fuzzy supersphere
Super Poisson-Lie symmetry of the GL(1|1) WZNW model and worldsheet boundary conditions
We show that the WZNW model on the Lie supergroup GL(1|1) has super
Poisson-Lie symmetry with the dual Lie supergroup B + A + A1;1|.i. Then, we
discuss about D-branes and worldsheet boundary conditions on supermanifolds, in
general, and obtain the algebraic relations on the gluing supermatrix for the
Lie supergroup case. Finally, using the supercanonical transformation
description of the super Poisson-Lie T-duality transformation, we obtain
formula for the description of the dual gluing supermatrix, then, we find the
gluing supermatrix for the WZNW model on GL(1|1) and its dual model. We also
discuss about different boundary conditions.Comment: 19 pages, two Refs. have adde
N=2 Current Algebras for Non-Semi-Simple Groups
We examine the problem of constructing N=2 superconformal algebras out of N=1
non-semi-simple affine Lie algebras. These N=2 superconformal theories share
the property that the super Virasoro central charge depends only on the
dimension of the Lie algebra. We find, in particular, a construction having a
central charge c=9. This provides a possible internal space for string
compactification and where mirror symmetry might be explored.Comment: 10 pages, BONN-HE-94-0
D-branes on Group Manifolds and Deformation Quantization
Recently M. Kontsevich found a combinatorial formula defining a star-product
of deformation quantization for any Poisson manifold. Kontsevich's formula has
been reinterpreted physically as quantum correlation functions of a topological
sigma model for open strings as well as in the context of D-branes in flat
backgrounds with a Neveu-Schwarz B-field. Here the corresponding Kontsevich's
formula for the dual of a Lie algebra is derived in terms of the formalism of
D-branes on group manifolds. In particular we show that that formula is encoded
at the two-point correlation functions of the Wess-Zumino-Witten effective
theory with Dirichlet boundary conditions. The B-field entering in the
formalism plays an important role in this derivation.Comment: 20 pages, harvmac file, no figures, corrected typo
On quasi-Jacobi and Jacobi-quasi bialgebroids
We study quasi-Jacobi and Jacobi-quasi bialgebroids and their relationships
with twisted Jacobi and quasi Jacobi manifolds. We show that we can construct
quasi-Lie bialgebroids from quasi-Jacobi bialgebroids, and conversely, and also
that the structures induced on their base manifolds are related via a quasi
Poissonization
A Vector Non-abelian Chern-Simons Duality
Abelian Chern-Simons gauge theory is known to possess a `-self-dual'
action where its coupling constant is inverted {\it i.e.} . Here a vector non-abelian duality is found in the
pure non-abelian Chern-Simons action at the classical level. The dimensional
reduction of the dual Chern-Simons action to two-dimensions constitutes a dual
Wess-Zumino-Witten action already given in the literature.Comment: 14+1 pages, LaTeX file, no figures, version to appear in Phys. Rev
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
The Fuzzy Supersphere
We introduce the fuzzy supersphere as sequence of finite-dimensional,
noncommutative -graded algebras tending in a suitable limit to a dense
subalgebra of the -graded algebra of -functions on
the -dimensional supersphere. Noncommutative analogues of the body map
(to the (fuzzy) sphere) and the super-deRham complex are introduced. In
particular we reproduce the equality of the super-deRham cohomology of the
supersphere and the ordinary deRham cohomology of its body on the "fuzzy
level".Comment: 33 pages, LaTeX, some typos correcte
T-Duality and Penrose limits of spatially homogeneous and inhomogeneous cosmologies
Penrose limits of inhomogeneous cosmologies admitting two abelian Killing
vectors and their abelian T-duals are found in general. The wave profiles of
the resulting plane waves are given for particular solutions. Abelian and
non-abelian T-duality are used as solution generating techniques. Furthermore,
it is found that unlike in the case of abelian T-duality, non-abelian T-duality
and taking the Penrose limit are not commutative procedures.Comment: 16 pages, 4 figures. Discussion on non-abelian T-duality expande