T-Duality in Arbitrary String Backgrounds

Abstract

T-Duality is a poorly understood symmetry of the space-time fields of string theory that interchanges long and short distances. It is best understood in the context of toroidal compactification where, loosely speaking, radii of the torus are inverted. Even in this case, however, conventional techniques permit an understanding of the transformations only in the case where the metric on the torus is endowed with Abelian Killing symmetries. Attempting to apply these techniques to a general metric appears to yield a non-local world-sheet theory that would defy interpretation in terms of space-time fields. However, there is now available a simple but powerful general approach to understanding the symmetry transformations of string theory, which are generated by certain similarity transformations of the stress-tensors of the associated conformal field theories. We apply this method to the particular case of T-Duality and i) rederive the known transformations, ii) prove that the problem of non-locality is illusory, iii) give an explicit example of the transformation of a metric that lacks Killing symmetries and iv) derive a simple transformation rule for arbitrary string fields on tori.

25 pages, plain Tex, new references added

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Cited by in corpus (17)

• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• Generalised T-Duality and Non-Geometric Backgrounds
• A ten-dimensional action for non-geometric fluxes
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• Non-Geometric Fluxes in Supergravity and Double Field Theory
• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality
• Dressing Cosets
• Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry
• Duality Symmetries and Noncommutative Geometry of String Spacetime
• Noncommutative Geometry and Spacetime Gauge Symmetries of String Theory
• From Loop Space Mechanics to Nonabelian Strings
• T-dualization in a curved background in absence of a global symmetry
• On deformations of 2d SCFTs
• Spacetime Supersymmetry in a nontrivial NS-NS Superstring Background
• Metastring Theory and Modular Space-time
• O(d,d,Z) Transformations as Automorphisms of the Operator Algebra
• Torus Bundles, Automorphisms and T-Duality