Noncommutative geometry and Matrix theory

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Published 19 February 1998 • Published under licence by IOP Publishing Ltd
, , Citation Alain Connes et al JHEP02(1998)003 DOI 10.1088/1126-6708/1998/02/003

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1 Institut des Hautes Études Scientifiques, Le Bois-Marie, Bures-sur-Yvette, 91440 France

2 Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08855--0849 USA

3 Department of Mathematics, University of California, Davis, CA 95616 USA

Dates

  1. Received 5 February 1998
  2. Accepted 5 February 1998
  3. Published

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Abstract

We study toroidal compactification of Matrix theory, using ideas and results of non-commutative 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 formulation of Matrix theory and its relation to the BFSS Matrix theory.

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