D-brane gauge theories from toric singularities of the form $C^3/\Gamma$ and $C^4/\Gamma$

TL;DR

This paper explores how D-branes probing specific toric singularities lead to gauge theories, analyzing examples from orbifolds of complex spaces to understand their geometric and physical properties.

Contribution

It provides explicit computations of world-volume gauge theories for D-branes on various toric singularities, expanding the understanding of gauge theories from geometric data.

Findings

Derived gauge theories from toric singularities of C^3 and C^4

Analyzed partial resolutions of specific orbifolds

Connected geometric data to gauge theory structures

Abstract

We discuss examples of D-branes probing toric singularities, and the computation of their world-volume gauge theories from the geometric data of the singularities. We consider several such examples of D-branes on partial resolutions of the orbifolds ${\bf C^3/Z_2\times Z_2}$,${\bf C^3/Z_2\times Z_3}$ and ${\bf C^4/Z_2\times Z_2 \times Z_2}$.