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 zeromodes and so can be expanded to give an infinite set of fields on the doubled torus. We use 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 Tduality acting on fields that have explicit dependence on the torus coordinates and the dual coordinates. We find that, along with gravity, a KalbRamond 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 September 2009
 DOI:
 10.1088/11266708/2009/09/099
 arXiv:
 arXiv:0904.4664
 Bibcode:
 2009JHEP...09..099H
 Keywords:

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