D4-branes on Complete Intersection in Toric Variety

TL;DR

This paper studies D4-branes on toric Calabi-Yau spaces, proposing a determinantal variety description for their world volume and analyzing the Higgs branch of the moduli space through quiver gauge theories and tachyon condensation.

Contribution

It introduces a novel determinantal variety framework for D4-brane world volumes and relates the Higgs branch to a quiver with doubled nodes from a D6-ar{D}6 system.

Findings

Proposes determinantal variety as D4-brane world volume

Describes Higgs branch via a quiver with doubled nodes

Recasts tachyon condensation in open string gauge linear sigma model

Abstract

We consider D4-branes on toric Calabi-Yau spaces. The quiver gauge theory that describes several D4-branes on the Calabi-Yau has a Higgs branch, that describes configurations of a single large D4-brane with the same charges. We propose that the world volume of such a D4-brane is described by a determinantal variety. We discuss a description of the Higgs branch of the moduli space in terms of a quiver with twice as many nodes and only bifundamental fields, arising from a $D6-\bar{D}6$ system. We recast the tachyon condensation of the $D6-\bar{D}6$ system in the language of open string gauge linear sigma model.