On Background Independence and Duality Invariance in String Theory

TL;DR

This paper demonstrates that at first order in alpha', a fully background independent and duality invariant formulation of bosonic string theory in terms of metric, b-field, and dilaton cannot be achieved, but it exists using frame variables with deformed transformations.

Contribution

It proves the non-existence of a background independent, duality invariant formulation in metric variables at first order in alpha', and introduces a formulation using deformed frame variables.

Findings

No consistent background independent gauge algebra at order alpha' in metric variables.

A background independent formulation exists with deformed frame transformations.

Implications for curved backgrounds like cosmology are discussed.

Abstract

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). Potential applications for curved backgrounds, as in cosmology, are discussed.