On T-duality transformations for the three-sphere

Abstract

We study collective T-duality transformations along one, two and three directions of isometry for the three-sphere with H-flux. Our aim is to obtain new non-geometric backgrounds along lines similar to the example of the three-torus. However, the resulting backgrounds turn out to be geometric in nature. To perform the duality transformations, we develop a novel procedure for non-abelian T-duality, which follows a route different compared to the known literature, and which highlights the underlying structure from an alternative point of view.

42 pages; v2: references added; v3: published version

References in corpus (61)

• M Theory, Orientifolds and G-Flux
• A Geometry for Non-Geometric String Backgrounds
• Duality, Quotients, and Currents
• Nongeometric Flux Compactifications
• Duality Symmetries from Non--Abelian Isometries in String Theories
• New Supersymmetric String Compactifications
• Dual Non-Abelian Duality and the Drinfeld Double
• Doubled Geometry and T-Folds
• Double Field Theory: A Pedagogical Review
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• Duality Twists, Orbifolds, and Fluxes
• Some Global Aspects of Duality is String Theory
• Geometric Constructions of Nongeometric String Theories
• T-duality, Generalized Geometry and Non-Geometric Backgrounds
• On non-abelian T-dual geometries with Ramond fluxes
• Generalised T-Duality and Non-Geometric Backgrounds
• On Nonabelian Duality
• On Non-Abelian Duality
• A ten-dimensional action for non-geometric fluxes
• T-Duality: Topology Change from H-flux
• T-duality for torus bundles via noncommutative topology
• Axial Vector Duality as a Gauge Symmetry and Topology Change in String Theory
• T-duality and closed string non-commutative (doubled) geometry
• A geometric action for non-geometric fluxes
• Nonassociative Gravity in String Theory?
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Nonassociative tori and applications to T-duality
• Constructing Nongeometric Vacua in String Theory
• Exact Duality Symmetries in CFT and String Theory
• Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory
• Non-Abelian T-duality and the AdS/CFT correspondence:new N=1 backgrounds
• Non-Geometric Fluxes in Supergravity and Double Field Theory
• Electric/Magnetic Deformations of S^3 and AdS_3, and Geometric Cosets
• On the Topology and Flux of T-Dual Manifolds
• Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
• Gauged WZW models and Non-abelian duality
• Non-Abelian Duality and Canonical Transformations
• Non-Abelian T-duality and consistent truncations in type-II supergravity
• Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
• T-duality for principal torus bundles
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes
• Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
• (Non-)commutative closed string on T-dual toroidal backgrounds
• Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry
• T-duality with H-flux: non-commutativity, T-folds and G x G structure
• Non-geometric Backgrounds and the First Order String Sigma Model
• On mysteriously missing T-duals, H-flux and the T-duality group
• A bi-invariant Einstein-Hilbert action for the non-geometric string
• Matrix theory origins of non-geometric fluxes
• Nongeometry, Duality Twists, and the Worldsheet
• Non-geometric String Backgrounds and Worldsheet Algebras
• Worldsheet CFTs for Flat Monodrofolds
• Warped anti-de Sitter spaces from brane intersections in type II string theory
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• Twisted Poisson Structures and Non-commutative/non-associative Closed String Geometry
• T-duality revisited
• Effective descriptions of branes on non-geometric tori
• Geometry and Duality in Supersymmetric sigma-Models
• Lie algebroids, non-associative structures and non-geometric fluxes

Cited by in corpus (15)

• Supersymmetry and non-Abelian T-duality in type II supergravity
• Non-geometric backgrounds in string theory
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Holographic Flows in non-Abelian T-dual Geometries
• Type IIB flux vacua and tadpole cancellation
• Beyond the standard gauging: gauge symmetries of Dirac Sigma Models
• Unwinding strings in semi-flatland
• T-duality without isometry via extended gauge symmetries of 2D sigma models
• The monodromy of T-folds and T-fects
• $O(d,d)$ transformations preserve classical integrability
• Strings in Singular Space-Times and their Universal Gauge Theory
• Towards a world-sheet description of doubled geometry in string theory
• Open-string T-duality and applications to non-geometric backgrounds
• T-duality transformations for the NS5-brane along angular directions
• Simultaneous T-dualization of type II pure spinor superstring