Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models

Abstract

Starting from the classification of 6-dimensional Drinfeld doubles and their decomposition into Manin triples we construct 3-dimensional Poisson-Lie T-dual or more precisely T-plural sigma models. Of special interest are those that are conformally invariant. Examples of models that satisfy vanishing beta-function equations with zero dilaton are presented and their duals are calculated. It turns out that for "traceless" dual algebras they satisfy the beta-function equations as well but usually with rather nontrivial dilaton. We also present explicit examples of several kinds of obstacles and difficulties present in construction of quantum dual models. Such concrete examples might be helpful in further development and improvement of quantum version of Poisson-Lie T-duality.

21 pages, minor typos corrected and clarifications added

References in corpus (4)

• Poisson-Lie T-plurality
• Classification of 6-dimensional real Drinfeld doubles
• On modular spaces of semisimple Drinfeld doubles
• One-loop renormalizability of all 2d dimensional Poisson-Lie sigma-models

Cited by in corpus (9)

• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Non-Abelian U-duality for membrane
• Classification of real three-dimensional Lie bialgebras and their Poisson-Lie groups
• Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models II: Nondiagonal metrics and dilaton puzzle
• The Poincaré group as a Drinfel'd double
• Jacobi-Lie T-plurality
• Cosmological string backgrounds from super Poisson-Lie T-plurality
• Poisson-Lie T-plurality for dressing cosets
• Classification of standard Manin triples in dimension 4+4