Double Metric, Generalized Metric and ${\alpha }^{\prime }$-Geometry

Abstract

We relate the unconstrained `double metric' of the `${\alpha }^{\prime }$-geometry' formulation of double field theory to the constrained generalized metric encoding the spacetime metric and b-field. This is achieved by integrating out auxiliary field components of the double metric in an iterative procedure that induces an infinite number of higher-derivative corrections. As an application we prove that, to first order in ${\alpha }^{\prime }$ and to all orders in fields, the deformed gauge transformations are Green-Schwarz-deformed diffeomorphisms. We also prove that to first order in ${\alpha }^{\prime }$ the spacetime action encodes precisely the Green-Schwarz deformation with Chern-Simons forms based on the torsionless gravitational connection. This seems to be in tension with suggestions in the literature that T-duality requires a torsionful connection, but we explain that these assertions are ambiguous since actions that use different connections are related by field redefinitions.

20 pages

References in corpus (8)

• Double Field Theory
• Double Field Theory Formulation of Heterotic Strings
• T-duality and ${\alpha }^{\prime }$-corrections
• Double Field Theory at Order ${\alpha }^{\prime }$
• Frame-like Geometry of Double Field Theory
• Heterotic Effective Action and Duality Symmetries Revisited
• Heterotic $\alpha$'-corrections in Double Field Theory
• Green-Schwarz mechanism and ${\alpha }^{\prime }$-deformed Courant brackets

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• Generalized Dualities and Higher Derivatives
• On the curious spectrum of duality invariant higher-derivative gravity
• On Background Independence and Duality Invariance in String Theory
• Background Independent Double Field Theory at Order ${\alpha }^{\prime }$: Metric vs. Frame-like Geometry
• The generalized Bergshoeff-de Roo identification II
• ${\alpha }^{\prime }$-corrections and their double formulation
• Heterotic Reduction of Courant Algebroid Connections and Einstein-Hilbert Actions
• An ${\alpha }^{\prime }$-complete theory of cosmology and its tensionless limit
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• Kaluza-Klein Reduction of Low-Energy Effective Actions: Geometrical Approach
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