D-Branes on Noncompact Calabi-Yau Manifolds: K-Theory and Monodromy

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  • 29 April 2001
Abstract
We study D-branes on smooth noncompact toric Calabi-Yau manifolds and give a simple recipe for determining a distinguished basis {S_i} for the compactly supported K-theory. If the Calabi-Yau manifold is a resolution of an abelian orbifold singularity this basis coincides with what has been found in the context of McKay correspondence, but our procedure works for any noncompact toric Calabi-Yau manifold. Using local mirror symmetry we demonstrate that the S_i have simple transformation properties under monodromy; in particular, they are the objects that generate monodromy around the principal component of the discriminant locus. One of our examples, the toric resolution of C^3/(Z_2 x Z_2), is a three parameter model for which we are able to give an explicit solution of the GKZ system.

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