Discrete Torsion, Covering Groups and Quiver Diagrams

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.

26 pages, 8 figures, some errors corrected

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• Quiver Gauge Theory and Conformality at the TeV Scale
• Lectures on D-branes, Gauge Theories and Calabi-Yau Singularities
• On Algebraic Singularities, Finite Graphs and D-Brane Gauge Theories: A String Theoretic Perspective
• Finite Heisenberg Groups from Nonabelian Orbifold Quiver Gauge Theories
• Discrete Torsion and Branes in M-theory from Mathematical Viewpoint
• Superstring Theory on pp Waves with ADE Geometries
• Resolution a la Kronheimer of ${\mathbb{C}}^3/\Gamma$ singularities and the Monge-Ampere equation for Ricci-flat Kaehler metrics in view of D3-brane solutions of supergravity
• Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
• McKay quivers and decomposition
• D-branes in Nonabelian Orbifolds with Discrete Torsion
• D3-brane supergravity solutions from Ricci-flat metrics on canonical bundles of Kähler-Einstein surfaces