Discrete Torsion, Non-Abelian Orbifolds and the Schur Multiplier

TL;DR

This paper classifies SU(n) orbifolds allowing discrete torsion using Schur Multiplier computations, introduces new non-cyclic torsion groups, and explores a non-Abelian dihedral orbifold with discrete torsion.

Contribution

It provides explicit classifications of SU(n) orbifolds with discrete torsion, including a novel non-cyclic torsion group and a non-Abelian dihedral orbifold example.

Findings

Identified new classes of orbifolds with discrete torsion.

Computed Schur Multipliers for classification.

Compared quiver theories of dihedral groups with and without discrete torsion.

Abstract

Armed with the explicit computation of Schur Multipliers, we offer a classification of SU(n) orbifolds for n = 2,3,4 which permit the turning on of discrete torsion. This is in response to the host of activity lately in vogue on the application of discrete torsion to D-brane orbifold theories. As a by-product, we find a hitherto unknown class of N = 1 orbifolds with non-cyclic discrete torsion group. Furthermore, we supplement the status quo ante by investigating a first example of a non-Abelian orbifold admitting discrete torsion, namely the ordinary dihedral group as a subgroup of SU(3). A comparison of the quiver theory thereof with that of its covering group, the binary dihedral group, without discrete torsion, is also performed.