Double sigma models

This thesis investigates the properties of the interacting chiral boson model for the maximally doubled string. We first introduce and briefly review double field theory. We then review two world-sheet actions for the doubled string: Tseytlin’s original duality symmetric string and a recent example of the double sigma model based on Hull’s doubled formalism, which is constructed to be equivalent to Tseytlin’s formulation. One feature of the latter concerns the underlying assumption of a base-fibre split, which means the fibre metric depends only on the base coordinates. In this thesis, we instead consider the case in which all coordinates are doubled. Taking the most general form of the Tseytlin action in which the fields possess arbitrary dependence on the full doubled geometry, we investigate whether a generic approach to the interacting chiral boson model - one which does not assume O(D,D) invariance from the outset - satisfies the requirement of conformal invariance at the quantum level. This demands that the doubled beta-functionals of the sigma model couplings vanish in the maximally doubled space.