Branes at Generalized Conifolds and Toric Geometry

TL;DR

This paper explores the relationship between D3 branes at generalized conifold singularities and type IIA D4 brane configurations using toric geometry, revealing how resolutions and dualities are geometrically realized.

Contribution

It provides a geometric interpretation of brane configurations and dualities in string theory through toric geometry analysis of generalized conifolds.

Findings

Resolutions of singularities correspond to NS brane movements.

Seiberg duality is realized by interchanging rotated NS branes.

Toric geometry effectively describes brane configurations and dualities.

Abstract

We use toric geometry to investigate the recently proposed relation between a set of D3 branes at a generalized conifold singularity and type IIA configurations of D4 branes stretched between a number of relatively rotated NS5 branes. In particular we investigate how various resolutions of the singularity corresponds to moving the NS branes and how Seiberg's duality is realized when two relatively rotated NS-branes are interchanged.