# Double Field Theory and String Duality

Chris Hull (Imperial Coll., London)

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

Theresienstrasse 37

Room 348/349