D-branes, Exceptional Sheaves and Quivers on Calabi-Yau manifolds: From Mukai to McKay
Suresh Govindarajan, T. Jayaraman
TL;DR
The authors develop a mutation-based framework to generate exceptional coherent sheaves on Calabi–Yau manifolds from a foundational helix built from large-volume monodromy acting on ${ m O}$, thereby reproducing the Gepner-point $ abla$-orbit with $ extstyle abla=igl( extstyle\sum_a l_a=0igr)$. They conjecture that all exceptional bundles arise by successive mutations of this helix and that restricting the mutated objects to the CY hypersurface yields the Gepner-state bundles; in parallel, they show how Beilinson-type quivers emerge in the large-volume regime and how the p-field in the GLSM recovers the McKay quiver at orbifold points. The approach is tested in multiple one- and two-parameter models, including ambient spaces with singularities not inherited by the CY, and the resulting RR-charge data match Gepner-model predictions. The work provides a canonical, phase-aware route to cataloging D-branes across GLSM phases via helices, mutations, and quiver gauge theories, linking geometric and LG/orbifold descriptions. Overall, the method offers a unifying picture of D-brane spectra through Beilinson/Mukai-type quivers and their McKay enhancements, with potential extensions to broader ambient geometries and bound-state structures.
Abstract
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 Kähler moduli space.