Noncommutative geometry and Matrix theory

1997/11/30 by Alain Connes, Michael R. Douglas, Albert Schwarz · 27 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Black Holes and Theoretical Physics #Commutative property #Compactification (mathematics) #Geometry #Mathematical physics #Mathematics #Matrix (chemical analysis) #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Physics #Pure mathematics #Supergravity #Supersymmetry #Theoretical physics #Torus #hep-th

paper · pdf · doi:10.1088/1126-6708/1998/02/003

published as JHEP 9802:003,1998 · harvmac, 41 pp. A slightly simpler BPS mass formula is proposed

openalex publication_date 1998/02/05 · arxiv created 1998/02/13 · arxiv updated 2010/11/19 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28

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.

Citations

• Projective Modules over Higher-Dimensional Non-Commutative Tori

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