Discrete torsion, non-abelian orbifolds and the Schur multiplier

Feng, B., Hanany, A., He, Y. & Prezas, N. (2001). Discrete torsion, non-abelian orbifolds and the Schur multiplier. Journal of High Energy Physics, 2001(JHEP01), doi: 10.1088/1126-6708/2001/01/033

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.