Double Field Theory and String Duality
18.02.2010 at 16:15
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. String field theory is used 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 level matching 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. Along with gravity, a Kalb-Ramond field and a dilaton must be added to support both usual and dual diffeomorphisms. A fully consistent and gauge invariant action on the doubled torus to cubic order in the fields is constructed. For the case in which the parameters and fields are T-dual to ones that have momentum but no winding, the action and gauge transformations are found to all orders. The gauge algebra for such restricted parameters is given by the Courant bracket. These algebras are realised as symmetries despite the failure of the Jacobi identity. The doubled geometry is physical and the dual dimensions should not be viewed as an auxiliary structure or a gauge artifact.
Arnold Sommerfeld Center