Discrete Torsion, Non-Abelian Orbifolds and the Schur Multiplier

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.

23 pages, 2 figures, references added and some typos corrected

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Cited by in corpus (19)

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• Discrete Torsion, Covering Groups and Quiver Diagrams
• D-branes on Singularities: New Quivers from Old
• Closed String Tachyons, Non-Supersymmetric Orbifolds and Generalised McKay Correspondence
• Lectures on D-branes, Gauge Theories and Calabi-Yau Singularities
• On Algebraic Singularities, Finite Graphs and D-Brane Gauge Theories: A String Theoretic Perspective
• Non Abelian orbifold compactifications of the heterotic string
• Finite Heisenberg Groups from Nonabelian Orbifold Quiver Gauge Theories
• Discrete Torsion and Branes in M-theory from Mathematical Viewpoint
• Metric Building of pp Wave Orbifold Geometries
• Cyclification of Orbifolds
• Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups
• Superstring Theory on pp Waves with ADE Geometries
• Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
• Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane
• McKay quivers and decomposition
• Generalised Clifford groups and simulation of associated quantum circuits