Background Independent Double Field Theory at Order ${\alpha }^{\prime }$: Metric vs. Frame-like Geometry

Abstract

The higher derivative corrections in double field theory are revisited to first order in ${\alpha }^{\prime }$. In first order perturbation theory around flat space, the gauge algebra is ${\alpha }^{\prime }$ corrected, governed by two parameters $a,b$. One parameter choice corresponds to bosonic string theory, another to heterotic string theory. These results are generalized to second order in perturbation theory by a Noether procedure. Using consistency conditions derived from the Jacobi identity, it is shown that for general $a,b$ there is no generalized metric formulation. A manifestly background independent formulation is instead given by a frame formalism, with ${\alpha }^{\prime }$-deformed frame transformations, as proposed by Marques and Nunez. Their construction is slightly generalized to an ${\alpha }^{\prime }$-deformed $GL(D)\times GL(D)$ frame formalism. The perturbation theory around flat space is matched to second order with the results obtained by the Noether procedure. We also obtain a formulation based on the `non-symmetric' metric $\mathcal{E}$, the sum of metric and $b$-field. The transformations of $\mathcal{E}$ under $O(D,D)$ receive non-trivial ${\alpha }^{\prime }$ corrections, unless $a=-b$, in which case there is a generalized metric formulation, in agreement with previous results in the literature.

46 pages, v2: minor changes, to appear in PRD

References in corpus (12)

• Double Field Theory
• Doubled Geometry and T-Folds
• $L_{\infty }$ Algebras and Field Theory
• Double Field Theory at Order ${\alpha }^{\prime }$
• Frame-like Geometry of Double Field Theory
• Heterotic Effective Action and Duality Symmetries Revisited
• Green-Schwarz mechanism and ${\alpha }^{\prime }$-deformed Courant brackets
• String Field Theory Solution for Any Open String Background
• Wilsonian Effective Action of Superstring Theory
• Second order higher-derivative corrections in Double Field Theory
• On the curious spectrum of duality invariant higher-derivative gravity
• On Background Independence and Duality Invariance in String Theory

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• $L_{\infty }$ Algebras and Field Theory
• Duality Invariant Cosmology to all Orders in ${\alpha }^{\prime }$
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• Duality Invariance and Higher Derivatives
• A new twist on heterotic string compactifications
• Cosmology at the top of the ${\alpha }^{\prime }$ tower
• On Background Independence and Duality Invariance in String Theory
• T-duality and high-derivative gravity theories: the BTZ black hole/string paradigm
• The generalized Bergshoeff-de Roo identification II
• Green-Schwarz Mechanism for String Dualities
• Slowly rotating and the accelerating ${\alpha }^{\prime }$-corrected black holes in four and higher dimensions
• O($D$,$D$)-covariant two-loop $\beta$-functions and Poisson-Lie T-duality
• Heterotic Kerr-Schild Double Field Theory and its double Yang-Mills formulation
• On Background Independence in String Theory