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arXiv · 1509.02930

Double Metric, Generalized Metric and $α'$-Geometry

Olaf Hohm·Barton Zwiebach
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Abstract

We relate the unconstrained `double metric' of the `$α'$-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 $α'$ and to all orders in fields, the deformed gauge transformations are Green-Schwarz-deformed diffeomorphisms. We also prove that to first order in $α'$ 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.

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Olaf Hohm, Barton Zwiebach. 2015-09-09. Double Metric, Generalized Metric and $α'$-Geometry. https://doi.org/10.1103/physrevd.93.064035

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