The $Z_k \times D_{k'}$ Brane Box Model

TL;DR

This paper constructs and verifies a non-Abelian Brane Box Model for a specific orbifold singularity, demonstrating how group-theoretic twists ensure consistency and match geometric methods.

Contribution

It introduces a consistent non-Abelian Brane Box Model for the $Z_k imes D_{k'}$ orbifold, addressing previous inconsistency issues through a novel group-theoretic approach.

Findings

Model matches geometrical methods

Group-theoretic twist resolves inconsistencies

Constructs a new class of non-Abelian models

Abstract

An example of a non-Abelian Brane Box Model, namely one corresponding to a $Z_k \times D_{k'}$ orbifold singularity of $\C^3$, is constructed. Its self-consistency and hence equivalence to geometrical methods are subsequently shown. It is demonstrated how a group-theoretic twist of the non-Abelian group circumvents the problem of inconsistency that arise from na\"{\i}ve attempts at the construction.