On Background Independence and Duality Invariance in String Theory

Understand

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 $\alpha'$ there is no manifestly background independent and duality invariant formulation of bosonic string theory in terms of 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 $\alpha'$ is inconsistent with the Jacobi identity.
• A background independent formulation exists instead for frame variables subject to $\alpha'$-deformed frame transformations (generalized Green-Schwarz transformations).