D-branes, Exceptional Sheaves and Quivers on Calabi-Yau manifolds: From Mukai to McKay

Details D-branes, Exceptional Sheaves and Quivers on Calabi-Yau manifolds: From Mukai to McKay D-branes, Exceptional Sheaves and Quivers on Calabi-Yau manifolds: From Mukai to McKay

2000-10-23

arxiv.org/abs/hep-th/0010196v2

Nucl.Phys. B600 (2001) 457-486

Physics

High Energy Physics

High Energy Physics - Theory

34+1 pages;LaTex;4 figures v2;comment on flops added;one figure and references added

Scientific paper

10.1016/S0550-3213(01)00062-1

We present a method based on mutations of helices which leads to the construction (in the large volume limit) of exceptional coherent sheaves associated with the $(\sum_al_a=0)$ orbits in Gepner models. This is explicitly verified for a few examples including some cases where the ambient weighted projective space has singularities not inherited by the Calabi-Yau hypersurface. The method is based on two conjectures which lead to the analog,in the general case, of the Beilinson quiver for $\BP^n$. We discuss how one recovers the McKay quiver using the gauged linear sigma model (GLSM) near the orbifold or Gepner point in K\"ahler moduli space.

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