Duality symmetric closed string theory and interacting chiral scalars

Abstract

We discuss a formulation of closed string theory which is based on the “doubled” set of string coordinates ( x = x + + x −, x ̃ = x + − x − ) and thus is manifestly invariant under the duality transformations. The free string action is taken to be the sum of the chiral scalar actions for the “left” and “right” parts of x and the string vacua are identified with the corresponding interacting 2d theories which are Weyl and local Lorentz invariant. We derive the conditions of (on-shell) local Lorentz invariance of a general “chiral” sigma model and show that they are satisfied, in particular, for the standard torus backgrounds and a class of “left”-“right” interacting chiral WZW models. We consider the scalar perturbation of the “free” vacuum (relating the “tachyonic” partition function to that of the generalized Coulomb gas), derive corresponding RG equations and discuss their interpretation in terms of the effective action for the fields in the ( x, x ̃ ) space. We also find the duality invariant analog of the Einstein term in the gravitational effective action.