Noncommutative tori, Yang-Mills and string theory
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.
Keywords
Cite
@article{arxiv.hep-th/0509021,
title = {Noncommutative tori, Yang-Mills and string theory},
author = {Anatoly Konechny},
journal= {arXiv preprint arXiv:hep-th/0509021},
year = {2007}
}
Comments
11 pages, Latex; to appear in Encyclopedia of Mathematical Physics to be published by Elsevier in 2006, referencing follows the guidelines of the publisher