T-Duality and Non-Local Supersymmetries

Abstract

We study the non-localization of extended worldsheet supersymmetry under T-duality, when the associated complex structure depends on the coordinate with respect to which duality is performed. First, the canonical transformation which implements T-duality is generalized to the supersymmetric non-linear $\sigma$-models. Then, we obtain the non-local object which replaces the complex structure in the dual theory and write down the condition it should satisfy so that the dual action is invariant under the non-local supersymmetry. For the target space, this implies that the supersymmetry transformation parameter is a non-local spinor. The analogue of the Killing equation for this non-local spinor is obtained. It is argued that in the target space, the supersymmetry is no longer realized in the standard way. The string theoretic origin of this phenomenon is briefly discussed.

19 pages, Latex. Some references, discussions and comments (mainly in setion 4) and a note added

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Cited by in corpus (32)

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• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality
• SO(d,d) Transformations of Ramond-Ramond Fields and Space-time Spinors
• Gauge Unification in Highly Anisotropic String Compactifications
• Non--Abelian Duality, Parafermions and Supersymmetry
• Poisson-Lie T-Duality and Supersymmetry
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Aspects of T-duality in Open Strings
• Killing-Yano Supersymmetry in String Theory
• Warped anti-de Sitter spaces from brane intersections in type II string theory
• An O(D,D) Invariant Hamiltonian Action for the Superstring
• Symmetries, Currents and Conservation Laws of Self-Dual Gravity
• T-duality of the Green-Schwarz superstring
• Geometry and Duality in Supersymmetric sigma-Models
• The Worldsheet Perspective of T-duality Symmetry in String Theory
• Worldsheet boundary conditions in Poisson-Lie T-duality
• A Note on T-duality in Heterotic String Theory
• T-duality for the sigma model with boundaries
• T-duality and Generalized Complex Geometry
• Hyperkähler, Bi-hypercomplex, Generalized Hyperkähler Structures and T-duality
• The Semi-Chiral Quotient, Hyperkahler Manifolds and T-duality
• Complex Structures, T-duality and Worldsheet Instantons in Born Sigma Models
• T-duality of NSR superstring: The worldsheet perspective
• Global aspects of the renormalization group and the Hierarchy problem
• T-Duality without Quantum Corrections
• Potentials and T-duality
• T-duality and Scattering of Stringy States
• Geometry of T-duality
• Probes in fluxbranes and supersymmetry breaking through Hodge-duality
• Plane-parallel waves as Jacobi-Lie models
• Killings, Duality and Characteristic Polynomials
• T-duality on Almost Hermitian Spaces