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. © 2012 SISSA.
CITATION STYLE
Hohm, O., & Zwiebach, B. (2012). On the Riemann tensor in double field theory. Journal of High Energy Physics, 2012(5). https://doi.org/10.1007/JHEP05(2012)126
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