JETP Letters

, Volume 99, Issue 1, pp 42–46 | Cite as

Line bundle twisted chiral de Rham complex, chiral Riemann-Roch formula and D-branes on toric manifolds

  • S. E. ParkhomenkoEmail author


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.


Line Bundle JETP Letter Open String Toric Variety Elliptic Genus 
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Copyright information

© Pleiades Publishing, Inc. 2014

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia
  2. 2.Moscow Institute of Physics and Technology (State University)Dolgoprudnyi, Moscow regionRussia

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