On the Riemann tensor in double field theory
By O. Hohm, B. Zwiebach. 2011
190 citations recorded by the source corpus.
A bstractDouble 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.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/3215fe19a79ed95bc91c9b1e17d9479d57b94be2
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Citations in the corpus
- Doubled α′-geometry (2013, methodology): “For example, it was seen in [21] that certain structures in Riemann-squared cannot be written in terms of the generalized metric.”
- Double field theory: a pedagogical review (2013, background): “BI in DFT were extensively discussed in [29].”
- Exploring double field theory (2013, methodology): “It was shown in [64, 65]–[68] that these constraints only determine some projections of the connections, leaving undetermined pieces which cannot be identified with the physical degrees of freedom.”
- Duality Symmetric String and M-Theory (2013, background): “71), this object is not a tensor, having an anomalous transformation [172]”
- Extended geometry and gauged maximal supergravity (2013, background): “This is the natural extension of the DFT definition of Ricci tensor introduced in [33, 34, 36, 37].”
- Gauged double field theory (2012, background): “Since then, DFT has been extended in many different ways [5][10].”
- Duality invariant M-theory: gauged supergravities and Scherk-Schwarz reductions (2012, background): “Describing the properties of these manifolds will be an interesting direction for future study – in [47] recent progress in this direction has been made in understanding how to “exponentiate” the local symmetries for the O(d, d) case relevant to DFT.”
- The spacetime of double field theory: Review, remarks, and outlook (2013, background): “It was soon realized, however, that the expected higher derivative corrections, in particular, the Riemann-squared terms were difficult to include while preserving the symmetries of the theory [44].”
- β-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework (2013, background): “More recent related work for the Opd, dq covariant formalisms appeared in [46, 47, 48, 32, 49], where a specific form of the generalized connection is sometimes chosen.”