Target Space Duality between Simple Compact Lie Groups and Lie Algebras under the Hamiltonian Formalism: I. Remnants of Duality at the Classical Level

Details Target Space Duality between Simple Compact Lie Groups and Lie Algebras under the Hamiltonian Formalism: I. Remnants of Duality at the Classical Level Target Space Duality between Simple Compact Lie Groups and Lie Algebras under the Hamiltonian Formalism: I. Remnants of Duality at the Classical Level

1995-03-31

arxiv.org/abs/hep-th/9503226v2

Commun.Math.Phys. 179 (1996) 185-214

Physics

High Energy Physics

High Energy Physics - Theory

Two references and related comments added, also some typos corrected. LaTeX and epsf.tex, 36 pages, 4 EPS figures included in

Scientific paper

10.1007/BF02103719

It has been suggested that a possible classical remnant of the phenomenon of target-space duality (T-duality) would be the equivalence of the classical string Hamiltonian systems. Given a simple compact Lie group $G$ with a bi-invariant metric and a generating function $\Gamma$ suggested in the physics literature, we follow the above line of thought and work out the canonical transformation $\Phi$ generated by $\Gamma$ together with an $\Ad$-invariant metric and a B-field on the associated Lie algebra $\frak g$ of $G$ so that $G$ and $\frak g$ form a string target-space dual pair at the classical level under the Hamiltonian formalism. In this article, some general features of this Hamiltonian setting are discussed. We study properties of the canonical transformation $\Phi$ including a careful analysis of its domain and image. The geometry of the T-dual structure on $\frak g$ is lightly touched.

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