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

TL;DR

This work provides an explicit gauged linear sigma model (GLSM) construction for B-type D-branes on Calabi–Yau manifolds that correspond to coherent sheaves realized as the cohomology of monads. It extends the (0,2) boundary formalism to complexes of arbitrary length by introducing boundary fermions and boundary contact terms, implementing large-volume monodromy and facilitating the realization of bound states. The authors demonstrate how monads and longer complexes yield a field-theoretic realization of vector bundles and more general sheaves, including detailed examples related to Recknagel–Schomerus states and their bound states, and they discuss moduli counting within these bound states. The approach connects the derived-category perspective on B-branes with explicit worldsheet constructions, enabling a concrete analysis of moduli and monodromies in the stringy regime and providing a framework for analyzing branes on Calabi–Yau manifolds in GLSM language.

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.