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

A Vector Non-abelian Chern-Simons Duality

Abelian Chern-Simons gauge theory is known to possess a `$S$-self-dual' action where its coupling constant $k$ is inverted {\it i.e.} $k \leftrightarrow {1 \over k}$. 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

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

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 $T$-duality, to a rich structure of the dual pairs of $D$-branes configurations in group manifolds. The $D$-branes are characterized by their shapes and certain two-forms living on them. The WZNW path integral for the interacting $D$-branes diagrams is unambiguously defined if the two-form on the $D$-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 $D$-brane submanifold. An example of the $SU(N)$ WZNW model is studied in some detail.Comment: 28 pages, LaTe

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