Line bundle twisted chiral de Rham complex, chiral Riemann-Roch formula and D-branes on toric manifolds
Abstract
I present 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 ℙ1, ℙ2 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 interpret 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.
- Publication:
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Soviet Journal of Experimental and Theoretical Physics Letters
- Pub Date:
- March 2014
- DOI:
- 10.1134/S0021364014010081
- Bibcode:
- 2014JETPL..99...42P