Discrete Torsion, Covering Groups and Quiver Diagrams

TL;DR

This paper introduces a simple algorithm to analyze gauge theories of D-branes on orbifolds with discrete torsion using only ordinary character tables, simplifying previous complex methods.

Contribution

It provides a straightforward computational approach to study discrete torsion effects in orbifold gauge theories without advanced algebraic machinery.

Findings

Presented an algorithm using character tables for gauge theory analysis

Constructed quiver diagrams for specific SU(3)-orbifolds with non-trivial Schur Multipliers

Simplified the study of discrete torsion in orbifold models

Abstract

Without recourse to the sophisticated machinery of twisted group algebras, projective character tables and explicit values of 2-cocycles, we here present a simple algorithm to study the gauge theory data of D-brane probes on a generic orbifold G with discrete torsion turned on. We show in particular that the gauge theory can be obtained with the knowledge of no more than the ordinary character tables of G and its covering group G*. Subsequently we present the quiver diagrams of certain illustrative examples of SU(3)-orbifolds which have non-trivial Schur Multipliers. The paper serves as a companion to our earlier work (arXiv:hep-th/0010023) and aims to initiate a systematic and computationally convenient study of discrete torsion.