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

Bobby Ezhuthachan·Suresh Govindarajan·T. Jayaraman
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Abstract

We study fractional 2p-branes and their intersection numbers in non-compact orbifolds as well the continuation of these objects in Kahler 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 hep-th/0401135. We thus demonstrate the equivalence of the B-type branes corresponding to linear boundary conditions in LG orbifolds, originally constructed in hep-th/9907131, 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.

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Bobby Ezhuthachan, Suresh Govindarajan, T. Jayaraman. 2005-06-27. A quantum McKay correspondence for fractional 2p-branes on LG orbifolds. https://doi.org/10.1088/1126-6708%2F2005%2F08%2F050

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