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Topological mirrors and quantum rings. (English) Zbl 0827.58073

Yau, Shing-Tung (ed.), Essays on mirror manifolds. Cambridge, MA: International Press. 96-119 (1992).
Summary: Aspects of duality and mirror symmetry in string theory are discussed. We emphasize, through examples, the importance of loop spaces of a deeper understanding of the geometrical origin of dualities in string theory. Moreover we show that mirror symmetry can be reformulated in very simple terms as the statement of equivalence of two classes of topological theories: Topological sigma models and topological Landau-Ginzburg models. Some suggestions are made for generalization of the notion of mirror symmetry.
For the entire collection see [Zbl 0816.00010].

MSC:

58Z05 Applications of global analysis to the sciences
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T70 Quantization in field theory; cohomological methods
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