D-particles on T^4/Z_n orbifolds and their resolutions

Abstract

We formulate the effective field theory of a D-particle on orbifolds of $T^4$ by a cyclic group as a gauge theory in a $V$-bundle over the dual orbifold. We argue that this theory admits Fayet-Iliopoulos terms analogous to those present in the case of noncompact orbifolds. In the $n=2$ case, we present some evidence that turning on such terms resolves the orbifold singularities and may lead to a $K3$ surface realized as a blow up of the fixed points of the cyclic group action.

34 pages, 3 figures; very minor typos corrected, 2 references added

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• Noncommutative Geometry and Matrix Theory: Compactification on Tori
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• Compactification of M(atrix) theory on noncommutative toroidal orbifolds
• D-brane probes on G2 Orbifolds
• On Non Commutative Calabi-Yau Hypersurfaces
• NC Calabi-Yau Manifolds in Toric Varieties with NC Torus fibration
• Matrix Theory Compactification on Noncommutative $T^4/Z_2$
• Toric Varieties with NC Toric Actions: NC Type IIA Geometry
• NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion