Noncommutative tori, Yang-Mills and string theory

Details Noncommutative tori, Yang-Mills and string theory Noncommutative tori, Yang-Mills and string theory

2005-09-02

arxiv.org/abs/hep-th/0509021v1

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, Latex; to appear in Encyclopedia of Mathematical Physics to be published by Elsevier in 2006, referencing follows th

Scientific paper

Noncommutative tori are among historically the oldest and by now the most developed examples of noncommutative spaces. Noncommutative Yang-Mills theory can be obtained from string theory. This connection led to a cross-fertilization of research in physics and mathematics on Yang-Mills theory on noncommutative tori. One important result stemming from that work is the link between T-duality in string theory and Morita equivalence of associative algebras. In this article we give an overview of the basic results in differential geometry of noncommutative tori. Yang-Mills theory on noncommutative tori, the duality induced by Morita equivalence and its link with the T-duality are discussed. Noncommutative Nahm transform for instantons is introduced.

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