On Background Independence and Duality Invariance in String Theory

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 ${\alpha }^{\prime }$ 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 ${\alpha }^{\prime }$ is inconsistent with the Jacobi identity. A background independent formulation exists instead for frame variables subject to ${\alpha }^{\prime }$-deformed frame transformations (generalized Green-Schwarz transformations). Potential applications for curved backgrounds, as in cosmology, are discussed.

4 pages, v2: refs. added, minor typos corrected, v3: minor changes, to be published in PRL

References in corpus (5)

• Double Field Theory
• Double Field Theory at Order ${\alpha }^{\prime }$
• Green-Schwarz mechanism and ${\alpha }^{\prime }$-deformed Courant brackets
• Wilsonian Effective Action of Superstring Theory
• Background Independent Double Field Theory at Order ${\alpha }^{\prime }$: Metric vs. Frame-like Geometry

Cited by in corpus (16)

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• The Odd story of ${\alpha }^{\prime }$-corrections
• Non-perturbative de Sitter vacua via ${\alpha }^{\prime }$ corrections
• Duality Invariance and Higher Derivatives
• T-duality and high-derivative gravity theories: the BTZ black hole/string paradigm
• Background Independent Double Field Theory at Order ${\alpha }^{\prime }$: Metric vs. Frame-like Geometry
• Cosmology at the top of the ${\alpha }^{\prime }$ tower
• The generalized Bergshoeff-de Roo identification II
• Green-Schwarz Mechanism for String Dualities
• Are nonperturbative AdS vacua possible in bosonic string theory?
• Old Dualities and New Anomalies
• ${\alpha }^{\prime }$-corrections to DBI action via T-duality constraint
• On Background Independence in String Theory
• $O(D,D)$-constraint on $D$-dimensional effective actions
• Duality invariant string beta functions at two loops
• A Loop Quantum Gravity Inspired Action for the Bosonic String and Emergent Dimensions at Large Scales