general mechanisms
electric-magnetic duality, Montonen-Olive duality, geometric Langlands duality
string-fivebrane duality
string-QFT duality
QFT-QFT duality:
effective QFT incarnations of open/closed string duality,
relating (super-)gravity to (super-)Yang-Mills theory:
Seiberg duality (swapping NS5-branes)
What has come to be called nonabelian T-duality (de la Ossa-Quevedo 92) or 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.
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).
While ordinary abelian T-duality is supposedly a full duality in string theory, in particular in that it is an equivalence on the string perturbation series to all orders of the squared string length/Regge slope $\alpha'$ and the string coupling constant $g_s$, it has apparently been shown by Martin Roček (citation?) that there are topological obstructions at higher genus for non-abelian T-duality, letting it break down in higher orders of $g_s$; and already a genus-0 (tree level) it apparently breaks down for the open string (i.e. on punctured disks) at some order of $\alpha'$.
But see Hassler 20, Borsato-Wulff 20.
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)
Relation to T-folds:
Mark Bugden, Non-abelian T-folds (arXiv:1901.03782)
Ladislav Hlavatý, Ivo Petr, T-folds as Poisson-Lie plurals (arXiv:2004.08387)
Discussion of the duality at the level of type II supergravity equations of motion is (using Riemannian geometry of Courant algebroids) due to
Branislav Jurco, Jan Vysoky, Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle, Journal of Geometry and Physics Volume 130, August 2018, Pages 1-26 (arXiv:1708.04079)
Pavol Ševera, Fridrich Valach, Courant algebroids, Poisson-Lie T-duality, and type II supergravities (arXiv:1810.07763)
and in relation to double field theory:
Discussion within a broader picture of dual higher gauge theories, including 4d electric-magnetic duality:
Discussion of non-abelian T-duality from a comprehensive picture of higher differential geometry, relating Kaluza-Klein compactification on principal ∞-bundles to double field theory, T-folds, type II geometry, exceptional geometry, etc.:
See also
Benjo Fraser, Dimitrios Manolopoulos, Konstantinos Sfetsos, Non-Abelian T-duality and Modular Invariance (arXiv:1805.03657)
Francesco Bascone, Franco Pezzella, Patrizia Vitale, Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation (arXiv:2004.12858)
Falk Hassler, Thomas B. Rochais $O(D,D)$-covariant two-loop β-functions and Poisson-Lie T-duality (arXiv:2011.15130)
Discussion in cosmology:
Generalization to U-duality in exceptional generalized geometry:
Emanuel Malek, Daniel C. Thompson, Energy Physics - Theory Poisson-Lie U-duality in Exceptional Field Theory (arxiv:1911.07833)
Chris D. A. Blair, Daniel C. Thompson, Sofia Zhidkova, Exploring Exceptional Drinfeld Geometries (arxiv:2006.12452)
In the context of the BMN matrix model:
Discussion of $\alpha'$-corrections:
Falk Hassler, Thomas Rochais, $\alpha'$-corrected Poisson-Lie T-duality (arXiv:2007.07897)
Riccardo Borsato, Linus Wulff, Quantum correction to Poisson-Lie and non-abelian T-duality (arXiv:2007.07902)
Last revised on March 31, 2021 at 04:55:44. See the history of this page for a list of all contributions to it.