Matrix Factorizations for Local F-Theory Models

TL;DR

This paper employs matrix factorizations to model branes at simple singularities in local F-theory, providing a resolution-independent framework that captures internal fluxes and complex bound states.

Contribution

It introduces a novel matrix factorization approach to describe branes in local F-theory models, avoiding singularity resolution and including fluxes and bound states.

Findings

Matrix factorizations correspond to nodes in ADE Dynkin diagrams.

Branes with fluxes are naturally represented as bound states of indecomposable factorizations.

The approach encodes information neglected in conventional F-theory treatments.

Abstract

I use matrix factorizations to describe branes at simple singularities as they appear in elliptic fibrations of local F-theory models. Each node of the corresponding Dynkin diagrams of the ADE-type singularities is associated with one indecomposable matrix factorization which can be deformed into one or more factorizations of lower rank. Branes with internal fluxes arise naturally as bound states of the indecomposable factorizations. Describing branes in such a way avoids the need to resolve singularities and encodes information which is neglected in conventional F-theory treatments. This paper aims to show how branes arising in local F-theory models around simple singularities can be described in this framework.