Fröhlich, Jürg; Gawȩdzki, Krzysztof Conformal field theory and geometry of strings. (English) Zbl 0826.58007 Feldman, J. (ed.) et al., Mathematical quantum theory I: Field theory and many body theory. Proceedings of the Canadian Mathematical Society annual seminar, held in Vancouver, Canada, August 4-14, 1993. Providence, RI: American Mathematical Society. CRM Proc. Lect. Notes. 7, 57-97 (1994). The subject of this pedagogical and highly readable article is a discussion of conformal field theory models (which may be considered as tree-level solutions of string theory) from the point of view of noncommutative geometry as introduced by A. Connes [Publ. Math., Inst. Hautes Étud. Sci. 62, 257-360 (1985; Zbl 0592.46056)]. Already the simplest sigma models (with target spaces \(S^1\) and \(T^2\), respectively) exhibit the “stringy” phenomena of target space duality and mirror symmetry. Further topics treated in detail are: Wess-Zumino- Witten and “coset” theories, supersymmetric conformal field theories in general with an introduction to noncommutative de Rham calculus, supersymmetric WZW and coset models, and the relation between \(N = 2\) supersymmetric conformal field theory models and Calabi-Yau geometry (which lies at the core of mirror symmetry).For the entire collection see [Zbl 0807.00020]. Reviewer: H.Rumpf (Wien) Cited in 1 ReviewCited in 15 Documents MSC: 46L85 Noncommutative topology 46L87 Noncommutative differential geometry 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 81T60 Supersymmetric field theories in quantum mechanics 46L51 Noncommutative measure and integration 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras 46L55 Noncommutative dynamical systems 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory Keywords:supersymmetry; conformal field theory; string theory; non-commutative geometry; sigma models; mirror symmetry Citations:Zbl 0592.46056 PDFBibTeX XMLCite \textit{J. Fröhlich} and \textit{K. Gawȩdzki}, in: Mathematical quantum theory I: field theory and many body theory. Proceedings of the Canadian Mathematical Society annual seminar, held in Vancouver, Canada, August 4-14, 1993. Providence, RI: American Mathematical Society. 57--97 (1994; Zbl 0826.58007) Full Text: arXiv