abstract duality: opposite category,
concrete duality: dual object, dualizable object, fully dualizable object, dualizing object
between higher geometry/higher algebra
Langlands duality, geometric Langlands duality, quantum geometric Langlands duality
A T-fold (Hull 04) is supposed to be a kind of space that locally looks like a Riemannian manifold equipped with a B-field, but which is glued together from these not just by diffeomorphisms (as a smooth manifold is) but also by T-duality transformations along some torus fibers.
The idea is that a T-fold is a target space for a string sigma-model that is only locally a Riemannian manifold but globally a more general kind of geometry. In the literature sometimes the term non-geometric backgrounds is used for such “generalized geometric” backgrounds.
It is expected that T-folds should have a description in terms of spaces that locally are fiber products of one torus fiber bundle with its T-dual. (One proposed formalization is that these are the total spaces of principal 2-bundles for the T-duality 2-group).
One may then consider local field theory on these double torus fibrations, and this is, or is closely related to, what is called double field theory (Hull 06).
A mathematical formlization of the idea of T-folds, in terms of principal 2-bundles for the T-duality 2-group (hence in higher differential geometry) is developed in Nikolaus-Waldorf 18.
The idea was originally introduced in
The relation to double field theory goes back to
Further developments are in
Chris Hull, Global Aspects of T-Duality, Gauged Sigma Models and T-Folds (arXiv:hep-th/0604178)
Aaron Bergman, Daniel Robbins, Ramond-Ramond Fields, Cohomology and Non-Geometric Fluxes (arXiv:0710.5158)
Dieter Lüst, Stefano Massai, Valentí Vall Camell, The monodromy of T-folds and T-fects (arXiv:1508.01193)
A precise global definition of T-folds as principal 2-bundles for the T-duality 2-group described in the nLab entry T-Duality and Differential K-Theory is given in
Thomas Nikolaus, T-Duality in K-theory and elliptic cohomology, talk at String Geometry Network Meeting, Feb 2014, ESI Vienna (website)
Thomas Nikolaus, Konrad Waldorf, Higher geometry for non-geometric T-duals (arXiv:1804.00677)
Discussion for nonabelian T-duality:
Last revised on January 15, 2019 at 01:56:25. See the history of this page for a list of all contributions to it.