Target Space Duality I: General Theory

Abstract

We develop a systematic framework for studying target space duality at the classical level. We show that target space duality between manifolds M and Mtilde arises because of the existence of a very special symplectic manifold. This manifold locally looks like M x Mtilde and admits a double fibration. We analyze the local geometric requirements necessary for target space duality and prove that both manifolds must admit flat orthogonal connections. We show how abelian duality, nonabelian duality and Poisson-Lie duality are all special cases of a more general framework. As an example we exhibit new (nonlinear) dualities in the case M = Mtilde = R^n.

LaTeX, 29 pages, 1 eps figure. Added a couple of references and corrected a couple of typos. An FAQ that discusses some subtle points may be found at <http://www.physics.miami.edu/~alvarez/papers/duality/>

References in corpus (5)

• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality
• Duality-invariant class of two-dimensional field theories
• Poisson structures on double Lie groups
• Hamiltonian Approach to Poisson Lie T-Duality
• Target Space Duality II: Applications

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• Generalised Kinematics for Double Field Theory
• On de Sitter Spacetime and String Theory
• Poisson-Lie Duality in the String Effective Action
• T-duality in Massive Integrable Field Theories: The Homogeneous and Complex sine-Gordon Models
• Target Space Duality II: Applications
• Pseudoduality in Sigma Models
• Target Space Pseudoduality Between Dual Symmetric Spaces
• Hamiltonian Loop Group Actions and T-Duality for group manifolds
• Aspects of Quantum Fermionic T-duality
• T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group
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• Bihamiltonity as origin of T-duality of the closed string model
• Poisson-Lie T-Duality and non trivial monodromies
• Searching for new homogeneous sine-Gordon theories using T-duality symmetries
• Target Space Duality: The Dilaton Field
• Renormalisability of non-homogeneous T-dualised sigma-models
• Target Space Duality III: Potentials