2011/12/22 by Olaf Hohm, Barton Zwiebach · 1 voice · 4 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Covariant transformation #Dilaton #Einstein tensor #Noncommutative and Quantum Gravity Theories #Ricci curvature #Riemann curvature tensor #Scalar curvature #Scalar–tensor theory #Tensor field #Weyl tensor #hep-th
paper · pdf · doi:10.1007/jhep05(2012)126
36 pages, v2: minor changes, ref. added, v3: appendix on frame formalism added, version to appear in JHEP
arxiv published 2011/12/22 · openalex publication_date 2012/05/01 · arxiv created 2012/05/25 · arxiv updated 2015/06/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.