Boundary Fermions, Coherent Sheaves and D-branes on Calabi-Yau manifolds

TL;DR

This paper develops a method to construct boundary conditions for B-type D-branes on Calabi-Yau manifolds within the gauged linear sigma model, linking them to coherent sheaves and boundary fermions, and explores their monodromy and bound states.

Contribution

It introduces a novel construction of boundary conditions for D-branes corresponding to complex coherent sheaves, including those from complexes of arbitrary length, within the gauged linear sigma model.

Findings

Constructed boundary conditions for D-branes as coherent sheaves using boundary fermions.

Implemented large-volume monodromy via boundary contact terms.

Demonstrated examples with bound states and moduli counting.

Abstract

We construct boundary conditions in the gauged linear sigma model for B-type D-branes on Calabi-Yau manifolds that correspond to coherent sheaves given by the cohomology of a monad. This necessarily involves the introduction of boundary fields, and in particular, boundary fermions. The large-volume monodromy for these D-brane configurations is implemented by the introduction of boundary contact terms. We also discuss the construction of D-branes associated to coherent sheaves that are the cohomology of complexes of arbitrary length. We illustrate the construction using examples, specifically those associated with the large-volume analogues of the Recknagel-Schomerus states with no moduli. Using some of these examples we also construct D-brane states that arise as bound states of the above rigid configurations and show how moduli can be counted in these cases.