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arXiv · hep-th/0509021

Noncommutative tori, Yang-Mills and string theory

Anatoly Konechny
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Abstract

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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Anatoly Konechny. 2005-09-02. Noncommutative tori, Yang-Mills and string theory. https://arxiv.org/abs/hep-th/0509021

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