We systematically study and obtain the large-volume analogues of fractional two-branes on resolutions of the orbifolds ℂ3/ℤ n. We also study a generalisation of the McKay correspondence proposed in hep-th/0504164 called the quantum McKay correspondence by constructing duals to the fractional two-branes. Details are explicitly worked out for two examples - the crepant resolutions of ℂ3/ ℤ3 and ℂ3/ℤ5. © SISSA 2006.

Suresh Govindarajan

Department Of Physics

Bobby Ezhuthachan

T. Jayaraman

Fulltext

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IIT Madras

Journal of High Energy Physics

We study fractional 2p -branes and their intersection numbers in non-compact orbifolds as well the continuation of these objects in Kähler moduli space to coherent sheaves in the corresponding smooth non-compact Calabi-Yau manifolds. We show that the restriction of these objects to compact Calabi-Yau hypersurfaces gives the new fractional branes in LG orbifolds constructed by Ashok et. al. in [13]. We thus demonstrate the equivalence of the B-type branes corresponding to linear boundary conditions in LG orbifolds, originally constructed in [2], to a subset of those constructed in LG orbifolds using boundary fermions and matrix factorization of the world-sheet superpotential. The relationship between the coherent sheaves corresponding to the fractional two-branes leads to a generalization of the McKay correspondence that we call the quantum McKay correspondence due to a close parallel with the construction of branes on non-supersymmetric orbifolds. We also provide evidence that the boundary states associated to these branes in a conformal field theory description corresponds to a sub-class of the boundary states associated to the permutation branes in the Gepner model associated with the LG orbifold. © SISSA 2005.

A quantum McKay correspondence for fractional 2p-branes on LG orbifolds

We construct boundary conditions in the gauged linear sigma model for B-type D-branes on Calabi-Yau manifolds that correspond to coherent sheaves given by the cohomology of a monad. This necessarily involves the introduction of boundary fields, and in particular, boundary fermions. The large-volume monodromy for these D-brane configurations is implemented by the introduction of boundary contact terms. We also discuss the construction of D-branes associated to coherent sheaves that are the cohomology of complexes of arbitrary length. We illustrate the construction using examples, specifically those associated with the large-volume analogues of the Recknagel-Schomerus states with no moduli. Using some of these examples we also construct D-brane states that arise as bound states of the above rigid configurations and show how moduli can be counted in these cases.

Nuclear Physics B

Boundary fermions, coherent sheaves and D-branes on Calabi-Yau manifolds

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 (∑ala=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 Pn. 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.

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

We consider D-branes wrapped around supersymmetric cycles of Calabi-Yau manifolds from the viewpoint of N=2 Landau-Ginzburg models with boundary as well as by consideration of boundary states in the corresponding Gepner models. The Landau-Ginzburg approach enables us to provide a target space interpretation for the boundary states. The boundary states are obtained by applying Cardy's procedure to combinations of characters in the Gepner models which are invariant under spectral flow. We are able to relate the two descriptions using common discrete symmetries occurring in the two descriptions. We thus provide an extension to the boundary, the bulk correspondence between Landau-Ginzburg orbifolds and the corresponding Gepner models. © 2000 Elsevier Science B.V.

Journal	Journal of High Energy Physics
Publisher	IOP
ISSN	10298479
Open Access	No