Background Independence and Duality Invariance in String Theory

Closed string theory exhibits an O(D, D) duality symmetry on tori, which in double field theory is manifest before compactification. I prove that to first order in a' there is no manifestly background independent and duality invariant formulation of bosonic string theory in terms of a metric, b field, and dilaton. To this end I use O(D, D) invariant second order perturbation theory around flat space to show that the unique background independent candidate expression for the gauge algebra at order a' is inconsistent with the Jacobi identity. A background independent formulation exists instead for frame variables subject to a'- deformed frame transformations ( generalized Green- Schwarz transformations). Potential applications for curved backgrounds, as in cosmology, are discussed.