Line bundle twisted chiral de Rham complex, chiral Riemann-Roch formula and D-branes on toric manifolds
S. E. Parkhomenko
Landau Institute for Theoretical Physics of the RAS, 142432 Chernogolovka, Russia
Moscow Institute of Physics and Technology, 141707 Dolgoprudny, Russia
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 , and Hirzebruch
surface. Based on these results I propose the elliptic genus expression
of the bundle twisted chiral de Rham complex
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.