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

Connes, Alain; Douglas, Michael R.; Schwarz, Albert

J. High Energy Phys. 1998, No. 2, Paper No. 3, 35 p. (1998).

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.

MSC:

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)