Line bundle twisted chiral de Rham complex and bound states of D-branes on toric manifolds

In this note we calculate elliptic genus in various examples of twisted chiral de Rham complex on two dimensional toric compact manifolds and Calabi-Yau hypersurfaces in toric manifolds. At first the elliptic genus is calculated for the line bundle twisted chiral de Rham complex on a compact smooth toric manifold and K3 hypersurface in \mathbb{P}^{3} . Then we twist chiral de Rham complex by sheaves localized on positive codimension submanifolds in \mathbb{P}^{2} and calculate in each case the elliptic genus. In the last example the elliptic genus of chiral de Rham complex on \mathbb{P}^{2} twisted by SL(N) vector bundle with instanton number k is calculated. In all cases considered we find the infinite tower of open string oscillator contributions of the corresponding bound state of D-branes and identify directly the open string boundary conditions and D-brane charges.Comment: 14 pages, LaTex, some comments and references adde

Poisson-Lie T-duality and N=2 superconformal WZNW models on compact groups

The supersymmetric generalization of Pisson-Lie T-duality in N=2 superconformal WZNW models on the compact groups is considered. It is shown that the role of Drinfeld's doubles play the complexifications of the corresponding compact groups. These complex doubles are used to define the natural actions of the isotropic subgroups forming the doubles on the group manifolds of the N=2 superconformal WZNW models. The Poisson- Lie T-duality in N=2 superconformal U(2)-WZNW model considered in details. It is shown that this model admits Poisson-Lie symmetries with respect to the isotropic subgroups forming Drinfeld's double Gl(2,C). Poisson-Lie T-duality transformation maps this model into itself but acts nontrivialy on the space of classical solutions. Supersymmetric generalization of Poisson-Lie T-duality in N=2 superconformal WZNW models on the compact groups of higher dimensions is proposed.Comment: 12 pages, latex, misprints correcte

Free-field Representations and Geometry of some Gepner models

The geometry of $k^{K}$ Gepner model, where $k+2=2K$ is investigated by free-field representation known as "bc\bet\gm"-system. Using this representation it is shown directly that internal sector of the model is given by Landau-Ginzburg $\mathbb{C}^{K}/\mathbb{Z}_{2K}$-orbifold. Then we consider the deformation of the orbifold by marginal anti-chiral-chiral operator. Analyzing the holomorphic sector of the deformed space of states we show that it has chiral de Rham complex structure of some toric manifold, where toric dates are given by certain fermionic screening currents. It allows to relate the Gepner model deformed by the marginal operator to the $\sigma$-model on CY manifold realized as double cover of $\mathbb{P}^{K-1}$ with ramification along certain submanifold.Comment: LaTex, 14 pages, some acknowledgments adde