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On the Riemann tensor in double field theory

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Abstract

Double field theory provides T-duality covariant generalized tensors that are natural extensions of the scalar and Ricci curvatures of Riemannian geometry. We search for a similar extension of the Riemann curvature tensor by developing a geometry based on the generalized metric and the dilaton. We find a duality covariant Riemann tensor whose contractions give the Ricci and scalar curvatures, but that is not fully determined in terms of the physical fields. This suggests that α′ corrections to the effective action require α′ corrections to T-duality transformations and/or generalized diffeomorphisms. Further evidence to this effect is found by an additional computation that shows that there is no T-duality invariant four-derivative object built from the generalized metric and the dilaton that reduces to the square of the Riemann tensor.

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Authors and Affiliations

  1. Arnold Sommerfeld Center for Theoretical Physics, Theresienstrasse 37, D-80333, Munich, Germany

    Olaf Hohm

  2. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, U.S.A.

    Barton Zwiebach

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  1. Olaf Hohm
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  2. Barton Zwiebach
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Correspondence to Olaf Hohm.

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ArXiv ePrint: 1112.5296

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Hohm, O., Zwiebach, B. On the Riemann tensor in double field theory. J. High Energ. Phys. 2012, 126 (2012). https://doi.org/10.1007/JHEP05(2012)126

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  • DOI: https://doi.org/10.1007/JHEP05(2012)126

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