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Poisson-Lie T-duality

Contents

Contents

Idea

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.

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).

As a partial duality of string theory

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 α\alpha' and the string coupling constant g sg_s, it has apparntly 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 sg_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 α\alpha'.

References

The original articles are

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

  • 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)

Discussion within a broader picture of dual higher gauge theories, including 4d electric-magnetic duality:

See also

Discussion of nonabelian T-folds:

Discussion in cosmology:

  • Ladislav Hlavatý, Ivo Petr, Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations (arxiv:1910.08436)

Last revised on October 21, 2019 at 00:44:40. See the history of this page for a list of all contributions to it.