Noncommutative geometry and matrix theory: Compactification on tori. (English) Zbl 1018.81052

Summary: We study toroidal compactification of Matrix theory, using ideas and results of noncommutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification of these backgrounds, and argue that they correspond in supergravity to tori with constant background three-form tensor field. The paper includes an introduction for mathematicians to the IKKT (Ishibashi-Kawai-Kitazawa-Tsuchiya) formulation of Matrix theory and its relation to the BFSS (Banks-Fischler-Shenker-Susskind) Matrix theory.


81T75 Noncommutative geometry methods in quantum field theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
46L87 Noncommutative differential geometry
58B34 Noncommutative geometry (à la Connes)
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