On the deformation quantization description of matrix compactifications

Matrix theory compactifications on tori have associated Yang-Mills theories on the dual tori with sixteen supercharges. A non-commutative description of these Yang-Mills theories based in deformation quantization theory is pr ovided. 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 Fedoso v's geometry of deformation quantization. (C) 1999 Elsevier Science B.V.