Target-space duality between simple compact Lie groups and Lie algebras under the Hamiltonian formalism: I. Remnants of duality at the classical level

Orlando Alvarez, Chien Hao Liu

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

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 Γ suggested in the physics literature, we follow the above line of thought and work out the canonical transformation Φ generated by Γ together with an Ad-invariant metric and a B-field on the associated Lie algebra g of G so that G and 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 Φ including a careful analysis of its domain and image. The geometry of the T-dual structure on g is lightly touched. We leave the task of tracing back the Hamiltonian formalism at the quantum level to the sequel of this paper.

Original languageEnglish (US)
Pages (from-to)185-213
Number of pages29
JournalCommunications in Mathematical Physics
Volume179
Issue number1
DOIs
StatePublished - 1996

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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