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

TL;DR

This paper introduces a quantum McKay correspondence linking fractional 2p-branes on LG orbifolds with coherent sheaves on Calabi-Yau manifolds, revealing new insights into brane constructions and their mathematical relationships.

Contribution

It generalizes the McKay correspondence to a quantum version for fractional branes in LG orbifolds, connecting boundary states and coherent sheaves.

Findings

Demonstrates the equivalence of certain B-type branes in LG orbifolds.

Establishes a quantum McKay correspondence for fractional 2p-branes.

Provides evidence linking boundary states to permutation branes in Gepner models.

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.