On the Deformation Quantization Description of Matrix Compactifications

Abstract

Matrix theory compactifications on tori have associated Yang-Mills theories on the dual tori with sixteen supercharges. A noncommutative description of these Yang-Mills theories based in deformation quantization theory is provided. We show that this framework allows a natural generalization of the `Moyal B-deformation' of the Yang-Mills theories to non-constant background B-fields on curved spaces. This generalization is described through Fedosov's geometry of deformation quantization.

25 pages, harvmac file, no figures, corrected typos, added references, one comment added in sec. 4

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• Issues in M(atrix) Theory Compactification
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• D-branes on Group Manifolds and Deformation Quantization
• Noncommutative Gauge Theories from Deformation Quantization
• Symplectic connections, Noncommutative Yang Mills theory and Supermembranes
• The QCD Membrane
• D0-branes in an H-field Background and Noncommutative Geometry
• Loop Equation and Wilson line Correlators in Non-commutative Gauge Theories
• Effective Action for D-branes on SU(2)/U(1) Gauged WZW Model