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\(T\)-duality and the moment map. (English) Zbl 0924.58132

’t Hooft, Gerard (ed.) et al., Quantum fields and quantum space time. Summer school, Cargèse, Corsica, France, July 22 - August 3, 1996. New York, NY: Plenum Publishing Corporation. NATO ASI Ser., Ser. B, Phys. 364, 323-329 (1997).
In previous papers [e.g., C. Klimcik, Nucl. Phys. B, Proc. Suppl. 46, 116-121 (1996)], the authors have argued that the \(T\)-duality of string theory is in fact a manifestation of the well-known duality in the category of Poisson-Lie groups at the classical level and of Hopf algebras (quantum groups) at the quantum level. In this paper, this connection is reviewed in a more algebraic than geometric way. As a new result, a moment map is constructed for the Poisson-Lie symmetry of the system consisting of open strings propagating in a Poisson group manifold.
For the entire collection see [Zbl 0894.00053].
Reviewer: H.Rumpf (Wien)

MSC:

58Z05 Applications of global analysis to the sciences
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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