Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality

Details Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality

1997-10-21

arxiv.org/abs/hep-th/9710163v2

Nucl.Phys. B517 (1998) 549-566

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, latex. Minor grammatical typos corrected. Version to appear in Nucl. Phys. B

Scientific paper

10.1016/S0550-3213(97)00823-7

We prove that a transformation, conjectured in our previous work, between phase-space variables in $\s$-models related by Poisson-Lie T-duality is indeed a canonical one. We do so by explicitly demonstrating the invariance of the classical Poisson brackets. This is the first example of a class of $\s$-models with no isometries related by canonical transformations. In addition we discuss generating functionals of canonical transformations in generally non-isometric, bosonic and supersymmetric $\s$-models and derive the complete set of conditions that determine them. We apply this general formalism to find the generating functional for Poisson-Lie T-duality. We also comment on the relevance of this work to D-brane physics and to quantum aspects of T-duality.

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