Double Field Theory and the Geometry of Duality

21 May 2012
String theory on a torus requires the introduction of dual coordinates conjugate to string winding number. This leads to physics and novel geometry in a doubled space. This will be compared to generalized geometry, which doubles the tangent space but not the manifold. For a d-torus,   string theory can be formulated in terms of an infinite tower of fields depending on both the d torus coordinates and the d dual coordinates. This talk focuses on a finite subsector  consisting of a metric and B-field (both d x d matrices) and a dilaton all depending on the 2d doubled torus coordinates. The double field theory is constructed and found to have a novel symmetry that reduces to diffeomorphisms and anti-symmetric tensor gauge transformations in certain circumstances. It also has manifest T-duality symmetry which provides a generalisation of the usual Buscher rules to backgrounds without isometries. The theory has a real dependence on the full doubled geometry:  the dual dimensions are not auxiliary. It is concluded that the doubled geometry is physical and dynamical.
  • String Theory Seminar