Witten, Edward Overview of \(K\)-theory applied to strings. (English) Zbl 1003.81020 Duff, Michael J. (ed.) et al., Strings 2000. Proceedings of the international superstrings conference, Ann Arbor, MI, USA, July 10-15, 2000. Singapore: World Scientific. 53-66 (2001). Summary: \(K\)-theory provides a framework for classifying Ramond-Ramond (RR) charges and fields. \(K\)-theory of manifolds has a natural extension to \(K\)-theory of noncommutative algebras, such as the algebras considered in noncommutative Yang-Mills theory or in open string field theory. In a number of concrete problems, the \(K\)-theory analysis proceeds most naturally if one starts out with an infinite set of D-branes, reduced by tachyon condensation to a finite set. This suggests that string field theory should be reconsidered for \(N=\infty\).For the entire collection see [Zbl 0966.00041]. Cited in 8 Documents MSC: 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81-02 Research exposition (monographs, survey articles) pertaining to quantum theory 83E30 String and superstring theories in gravitational theory 19M05 Miscellaneous applications of \(K\)-theory 81T13 Yang-Mills and other gauge theories in quantum field theory Keywords:Ramond-Ramond (RR) charges and fields; noncommutative algebras; noncommutative Yang-Mills theory; D-branes; tachyon condensation PDFBibTeX XMLCite \textit{E. Witten}, in: Strings 2000. Proceedings of the international superstrings conference, Ann Arbor, MI, USA, July 10--15, 2000. Singapore: World Scientific. 53--66 (2001; Zbl 1003.81020)