What has come to be called nonabelian T-duality (Ossa-Quevedo 92) Poisson-Lie T-Duality (due to Klimcik-Ševera 95, von Unge 02) is a generalization of T-duality from fiber bundles equipped with an abelian group of isometries (torus bundles) to those with a nonabelian group of isometries.
It has been proven that these generalized T-dualities are are/induce equivalences of the corresponding string sigma-models at the level of classical field theory. However it seems to be open, and in fact questionable, that away from standard T-duality this yields an equivalence at the level of worldsheet quantum field theories, hence it is open whether Poisson-Lie/non-abelian T-duality is really a duality operation on perturbative string theory vacua.
Poisson-Lie T-duality may also be made manifest at the level of type II supergravity in the framework of double field theory on group manifolds. Using this framework both the NS/NS sector and the R/R sector are captured, and this allows to derive the transformation of the RR fields for full Poisson-Lie T-duality (Hassler 17).
The original articles are
Xenia C. de la Ossa, Fernando Quevedo, Duality Symmetries from Non–Abelian Isometries in String Theories, Nucl.Phys. B403 (1993) 377-394 (hep-th/9210021)
Ctirad Klimcik, Pavol Ševera, Dual non-Abelian duality and the Drinfeld double, Physics Letters B, Volume 351, Issue 4, 1 June 1995, Pages 455-462 (doi:10.1016/0370-2693(95)00451-P)
Rikard von Unge, Poisson-Lie T-plurality, Journal of High Energy Physics, Volume 2002, JHEP07 (2002) (arXiv:hep-th/0205245)
Review includes
I. Petr, From Buscher Duality to Poisson‐Lie T‐Plurality on Supermanifolds, AIP Conference Proceedings 1307, 119 (2010) (doi:10.1063/1.3527407)
Konstadinos Sfetsos, Recent developments in non-Abelian T-duality in string theory, Fortschr. Phys., Special Issue: Proceedings of the “Schools and Workshops on Elementary Particle Physics and Gravity” (CORFU 2010), 29 August – 12 September 2010, Corfu (Greece) Volume59, Issue11‐12 (arXiv:1105.0537)
See also
Discussion of the duality at the level of type II supergravity equations of motion is (using Riemannian geometry of Courant algebroids) due to
See also
Pavol Ševera, Fridrich Valach, Courant algebroids, Poisson-Lie T-duality, and type II supergravities (arXiv:1810.07763)
Falk Hassler, Poisson-Lie T-Duality in Double Field Theory (arXiv:1707.08624)
Discussion of nonabelian T-folds:
Last revised on January 15, 2019 at 01:50:36. See the history of this page for a list of all contributions to it.