T-duality for torus bundles via noncommutative topology
arXiv:hep-th/0401168 · doi:10.1007/s00220-004-1159-7
Abstract
It is known that the T-dual of a circle bundle with H-flux (given by a Neveu-Schwarz 3-form) is the T-dual circle bundle with dual H-flux. However, it is also known that torus bundles with H-flux do not necessarily have a T-dual which is a torus bundle. A big puzzle has been to explain these mysterious "missing T-duals.'' Here we show that this problem is resolved using noncommutative topology. It turns out that every principal 2-torus-bundle with H-flux does indeed have a T-dual, but in the missing cases (which we characterize), the T-dual is non-classical and is a bundle of noncommutative tori. The duality comes with an isomorphism of twisted K-theories, just as in the classical case. The isomorphism of twisted cohomology which one gets in the classical case is replaced by an isomorphism of twisted cyclic homology.
16 pages, Latex2e, 1 figure
References in corpus (3)
Cited by in corpus (91)
- Nongeometric Flux Compactifications
- T-duality, Generalized Geometry and Non-Geometric Backgrounds
- Hitchin Functionals in N=2 Supergravity
- SU(3) x SU(3) compactification and mirror duals of magnetic fluxes
- Generalized N=1 Orientifold Compactifications and the Hitchin functionals
- Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
- Nonassociative tori and applications to T-duality
- The GL(1|1) WZW model: From Supergeometry to Logarithmic CFT
- Gauged Supergravities
- Non-Geometric Fluxes in Supergravity and Double Field Theory
- Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
- Lectures on Nongeometric Flux Compactifications
- Non-geometric backgrounds in string theory
- Towards Minkowski Vacua in Type II String Compactifications
- Toroidal Orientifolds in IIA with General NS-NS Fluxes
- D-branes in Nongeometric Backgrounds
- 3-Cocycles, Non-Associative Star-Products and the Magnetic Paradigm of R-Flux String Vacua
- (Non-)commutative closed string on T-dual toroidal backgrounds
- T-duality with H-flux: non-commutativity, T-folds and G x G structure
- Matrix theory origins of non-geometric fluxes
- Non-commutative tori and Fourier-Mukai duality
- Generalized complex geometry and T-duality
- Principal noncommutative torus bundles
- The topology of T-duality for T^n-bundles
- Differential K-theory. A survey
- Extended Riemannian Geometry I: Local Double Field Theory
- Heterotic-type IIA duality with fluxes
- D-Branes, RR-Fields and Duality on Noncommutative Manifolds
- T-duality, Gerbes and Loop Spaces
- T-duality simplifies bulk-boundary correspondence
- A Dixmier-Douady classification for Fell algebras
- T-duality revisited
- Effective descriptions of branes on non-geometric tori
- Topology Change from (Heterotic) Narain T-Duality
- Introductory Lectures on Extended Supergravities and Gaugings
- Noncommutative gauge theories on D-branes in non-geometric backgrounds
- On T-duality transformations for the three-sphere
- Towards mirror symmetry à la SYZ for generalized Calabi-Yau manifolds
- T-duality simplifies bulk-boundary correspondence: some higher dimensional cases
- N=1 domain wall solutions of massive type II supergravity as generalized geometries
- Non-abelian T-folds
- T-duality simplifies bulk-boundary correspondence: the noncommutative case
- T-duality, Quotients and Currents for Non-Geometric Closed Strings
- Dual Gauged Supergravities
- Nonassociative geometry and twist deformations in non-geometric string theory
- Duality for topological abelian group stacks and T-duality
- Spherical T-Duality
- Group dualities, T-dualities, and twisted K-theory
- A walk in the noncommutative garden
- String theory on elliptic curve orientifolds and KR-theory
- Remarks on anomalous symmetries of C*-algebras
- C*-algebras in tensor categories
- Towards a world-sheet description of doubled geometry in string theory
- T-duality of current algebras and their quantization
- Topological T-duality for torus bundles with monodromy
- T-Duality as a Duality of Loop Group Bundles
- Topological T-Duality for Twisted Tori
- Twisted crystallograpic T-duality via the Baum--Connes isomorphism
- Part I, Free Actions of Compact Abelian Groups on C*-Algebras
- Crystallographic T-duality
- Real Baum-Connes assembly and T-duality for torus orientifolds
- Higher geometry for non-geometric T-duals
- T-duality for circle bundles via noncommutative geometry
- T-duality and Differential K-Theory
- Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality
- T-duality and the bulk-boundary correspondence
- Parametrised strict deformation quantization of C*-bundles and Hilbert C*-modules
- Higher nonunital Quillen K'-theory, KK-dualities and applications to topological -dualities
- Topological A-Type Models with Flux
- Open-string T-duality and applications to non-geometric backgrounds
- Deformations of Azumaya algebras
- Lie algebroids, non-associative structures and non-geometric fluxes
- T-duality for principal torus bundles and dimensionally reduced Gysin sequences
- Homology and K--Theory Methods for Classes of Branes Wrapping Nontrivial Cycles
- Generalised contact geometry as reduced generalised complex geometry
- A new approach to topological T-duality for principal torus bundles
- Exotic Courant algebroids and T-duality
- Topological T-duality, Automorphisms and Classifying Spaces
- Equivariant Topological T-Duality
- Open-String Non-Associativity in an R-flux Background
- Topological T-duality for Stacks using a Gysin Sequence
- A Chern-Weil Isomorphism for the Equivariant Brauer Group
- On the Chern character in Higher Twisted K-theory and spherical T-duality
- T-duality and the exotic chiral de Rham complex
- Topological T-duality and T-folds
- D-branes, KK-theory and duality on noncommutative spaces
- A Cech Dimensionally Reduced Gysin Sequence for Principal Torus Bundles
- Duality Covariant Solutions in Extended Field Theories
- Eight-dimensional non-geometric heterotic strings and enhanced gauge groups
- Dixmier-Douady for Dummies
- Crossed module actions on continuous trace -algebras