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VOLUME 99 (2014) | ISSUE 1 | PAGE 45
Line bundle twisted chiral de Rham complex, chiral Riemann-Roch formula and D-branes on toric manifolds
I represent the results of the elliptic genus calculations in various examples of twisted chiral de Rham complex on one- and two-dimensional toric compact manifolds. The explicit calculations are made for line bundle twisted chiral de Rham complex on \mathbb{P}^{1}, \mathbb{P}^{2} and Hirzebruch surface. Based on these results I propose the elliptic genus expression of the bundle twisted chiral de Rham complex for general smooth compact two dimensional toric manifold. The expression resembles Riemann-Roch formula and coincides with the later in certain limit. I interprete the result in terms of infinite tower of open string oscillator contributions and identify directly the open string boundary conditions of the corresponding bound state of D-branes.