Global Aspects of T-Duality, Gauged Sigma Models and T-Folds

Abstract

The gauged sigma-model argument that string backgrounds related by T-dual give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to obstructions to T-duality, but these are milder than those for gauging: it is possible to T-dualise a large class of sigma-models that cannot be gauged. For backgrounds that are torus fibrations, it is expected that T-duality can be applied fibrewise in the general case in which there are no globally-defined Killing vector fields, so that there is no isometry symmetry that can be gauged; the derivation of T-duality is extended to this case. The T-duality transformations are presented in terms of globally-defined quantities. The generalisation to non-geometric string backgrounds is discussed, the conditions for the T-dual background to be geometric found and the topology of T-folds analysed.

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References in corpus (31)

• Target Space Duality in String Theory
• 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
• Duality Twists, Orbifolds, and Fluxes
• Some Global Aspects of Duality is String Theory
• Reduction of Courant algebroids and generalized complex structures
• Geometric Constructions of Nongeometric String Theories
• Generalised T-Duality and Non-Geometric Backgrounds
• On Nonabelian Duality
• On Non-Abelian Duality
• Generalized Duality in Curved String-Backgrounds
• T-Duality: Topology Change from H-flux
• T-duality for torus bundles via noncommutative topology
• A Canonical Approach to Duality Transformations
• Axial Vector Duality as a Gauge Symmetry and Topology Change in String Theory
• Nonassociative tori and applications to T-duality
• Constructing Nongeometric Vacua in String Theory
• Dual String Pairs With N=1 And N=2 Supersymmetry In Four Dimensions
• On the Topology and Flux of T-Dual Manifolds
• Massive String Theories From M-Theory and F-Theory
• T-duality for principal torus bundles
• On mysteriously missing T-duals, H-flux and the T-duality group
• Massive IIA String Theory and Matrix Theory Compactification
• Nongeometry, Duality Twists, and the Worldsheet
• Gauged Wess-Zumino terms and Equivariant Cohomology
• Equivariant Cohomology and Gauged Bosonic sigma-Models
• Gauging the Wess-Zumino term of a sigma model with boundary
• Duality as a Gauge Symmetry and Topology Change

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