Double Field Theory

Abstract

The zero modes of closed strings on a torus --the torus coordinates plus dual coordinates conjugate to winding number-- parameterize a doubled torus. In closed string field theory, the string field depends on all zero-modes and so can be expanded to give an infinite set of fields on the doubled torus. We use the string field theory to construct a theory of massless fields on the doubled torus. Key to the consistency is a constraint on fields and gauge parameters that arises from the L_0 - \bar L_0=0 condition in closed string theory. The symmetry of this double field theory includes usual and 'dual diffeomorphisms', together with a T-duality acting on fields that have explicit dependence on the torus coordinates and the dual coordinates. We find that, along with gravity, a Kalb-Ramond field and a dilaton must be added to support both usual and dual diffeomorphisms. We construct a fully consistent and gauge invariant action on the doubled torus to cubic order in the fields. We discuss the challenges involved in the construction of the full nonlinear theory. We emphasize that the doubled geometry is physical and the dual dimensions should not be viewed as an auxiliary structure or a gauge artifact.

51 pages. v2: Corrected typo in eqn. (2.48) and very minor typos elsewhere. Added ref. [9] to M. Van Raamsdonk

References in corpus (8)

• Doubled Geometry and T-Folds
• Generalized complex geometry
• Background Field Equations for the Duality Symmetric String
• Worldsheet Instanton Corrections to the Kaluza-Klein Monopole
• Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions
• Worldsheet CFTs for Flat Monodrofolds
• Quantum Mechanics of the Doubled Torus
• Field Redefinitions, T-duality and Solutions in Closed String Field Theories

Cited by in corpus (16)

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• T-duality and closed string non-commutative (doubled) geometry
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• Double field formulation of Yang-Mills theory
• U-dual fluxes and Generalized Geometry
• E11, generalised space-time and IIA string theory
• The KK-Monopole/NS5-Brane in Doubled Geometry
• First order parent formulation for generic gauge field theories
• Non-singular string cosmology in a 2d Hybrid model
• T-duality of anomalous Chern-Simons couplings
• Parent formulation at the Lagrangian level
• Theory of Superdualities and the Orthosymplectic Supergroup
• Duality Symmetry of String Theory: A Worldsheet Perspective
• Superstring field theory equivalence: Ramond sector