Line bundle twisted chiral de Rham complex and bound states of D-branes on toric manifolds
arXiv:1307.0080 · doi:10.1016/j.nuclphysb.2014.02.003
Abstract
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.
14 pages, LaTex, some comments and references added