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

TL;DR

This paper investigates D-branes on noncompact toric Calabi-Yau manifolds, revealing how their K-theory basis transforms under monodromy and providing explicit solutions in a specific example.

Contribution

It demonstrates the monodromy properties of K-theory basis elements for D-branes using local mirror symmetry, including explicit solutions for a complex example.

Findings

K-theory basis elements transform simply under monodromy

Basis elements generate monodromy around the discriminant locus

Explicit GKZ system solutions for a specific toric resolution

Abstract

We study D-branes on smooth noncompact toric Calabi-Yau manifolds that are resolutions of abelian orbifold singularities. Such a space has a distinguished basis {S_i} for the compactly supported K-theory. 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.