Journal of High Energy Physics

, 2012:126

On the Riemann tensor in double field theory


DOI: 10.1007/JHEP05(2012)126

Cite this article as:
Hohm, O. & Zwiebach, B. J. High Energ. Phys. (2012) 2012: 126. doi:10.1007/JHEP05(2012)126


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.


Gauge SymmetryString DualityDifferential and Algebraic Geometry

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.Arnold Sommerfeld Center for Theoretical PhysicsMunichGermany
  2. 2.Center for Theoretical PhysicsMassachusetts Institute of TechnologyCambridgeU.S.A.