Kronecker foliation, D1-branes and Morita equivalence of Noncommutative two-tori | Zendy

Hiroshige Kajiura | Zendy

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Kronecker foliation, D1-branes and Morita equivalence of Noncommutative two-tori

Author(s) -

Hiroshige Kajiura

Publication year - 2002

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2002/08/050

Subject(s) - noncommutative geometry , morita equivalence , morita therapy , kronecker delta , foliation (geology) , equivalence (formal languages) , torus , mathematics , pure mathematics , geometry , geology , physics , paleontology , quantum mechanics , metamorphic rock

It is known that the physics of open strings on a D2-brane on a two-torus isrealized from the viewpoint of deformation quantization in the Seiberg-Wittenlimit. We study its T-dual theory, i.e. D1-brane physics on two-tori. Suchtheory is described by Kronecker foliation. The algebra of open strings on theD1-brane is then identified with the crossed product representation of anoncommutative two-torus. The Morita equivalence of noncommutative two-tori isalso realized geometrically along this line. As an application, Heisenbergmodules and the tensor product between them are discussed from these geometricviewpoints. We show they are related to the homological mirror symmetry oftwo-tori.Comment: 29 pages, 7 figure

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