D-branes on Stringy Calabi-Yau Manifolds

TL;DR

This paper connects D-branes in Gepner models with fractional branes in Landau-Ginzburg orbifolds, using the McKay correspondence to identify their K-theory classes without mirror symmetry, and verifies this with a Calabi-Yau example.

Contribution

It introduces a method to identify D-branes as fractional branes via the McKay correspondence, bypassing mirror symmetry calculations.

Findings

Identification of D-branes with coherent sheaves in the large volume limit

Calculation of K-theory classes for D-branes

Validation against mirror symmetry results for a specific Calabi-Yau hypersurface

Abstract

We argue that D-branes corresponding to rational B boundary states in a Gepner model can be understood as fractional branes in the Landau-Ginzburg orbifold phase of the linear sigma model description. Combining this idea with the generalized McKay correspondence allows us to identify these states with coherent sheaves, and to calculate their K-theory classes in the large volume limit, without needing to invoke mirror symmetry. We check this identification against the mirror symmetry results for the example of the Calabi-Yau hypersurface in $\WP^{1,1,2,2,2}$.