D-branes, exceptional sheaves and quivers on Calabi–Yau manifolds: from Mukai to McKay

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 ( a l 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 CalabiYau hypersurface. The method is based on two conjectures which lead to the analog,in the general case, of the Beilinson quiver for P 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.

Split attractor flows and the spectrum of BPS D-branes on the quintic

“…16 In the quintic case at hand, we find at the Gepner side λ G = 1 2 (5+ √ 21) ≈ 4.79129, and at the LCS side λ L = −1/λ G . The resulting monodromy stable spectrum at the Gepner side is shown in fig.…”

“…The former has been studied by far the most, as it provides a direct, powerful and extensive framework, firmly rooted in geometry and string theory. A partial list of references is [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. The alternative approach, based on the four dimensional low energy effective N = 2 supergravity theory, has received considerably less attention, in part because at first sight this effective theory seemed much too simple to be able to capture the intricacies of the D-brane spectrum.…”

Consistency of orbifold conformal field theories on $K3$

“…For the cyclic groups, we are in agreement with [Asp95] (G = Z 2 ), and with [Dou97,BI97] where mass formulae and tadpole cancellation conditions for D-branes were used; the author did not find the explicit results for the binary dihedral and tetrahedral groups in the literature. Theorem 3.3 indicates a connection to the classical McKay correspondence [McK80,McK81], which has also inspired very recent work in the physics literature [DD,GJ01,Tom01,May01]. All of the latter publications concentrate on higher dimensional cases where large volume limits are used, though.…”

Towards open string mirror symmetry for one-parameter Calabi-Yau hypersurfaces

“…At the Gepner point, a subset of the matrix factorizations can be identified [46] with the Recknagel-Schomerus boundary states | L, M, S B [47,48] in the corresponding Gepner model. The relation between D-branes on the last three families X in (2.22) and boundary states in the corresponding Gepner model has been studied in [49] which will be useful along the way (for related work see [50,51]). This will be explained in more detail in Section 3.1, where we will also specify the matrix factorizations for the various W in (2.25).…”