Towards a double field theory on para-Hermitian manifolds

@article{Vaisman2013TowardsAD,
  title={Towards a double field theory on para-Hermitian manifolds},
  author={Izu Vaisman},
  journal={Journal of Mathematical Physics},
  year={2013},
  volume={54},
  pages={123507}
}
  • I. Vaisman
  • Published 2 September 2012
  • Mathematics
  • Journal of Mathematical Physics
In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kahler manifolds. In this paper, we show that the same geometric constructions can be made on any para-Hermitian manifold. The field is interpreted as a compatible (pseudo-)Riemannian metric. The tangent bundle of the manifold has a natural, metric-compatible bracket that extends the C-bracket of double field theory. In the para-Kahler case, this bracket is equal to the sum of… 
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54 Citations
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54 Citations

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References

SHOWING 1-10 OF 25 REFERENCES
Homogeneous para-Kähler Einstein manifolds
A para-Kahler manifold can be defined as a pseudo-Riemannian manifold with a parallel skew-symmetric para-complex structure , that is, a parallel field of skew-symmetric endomorphisms with or,…
Towards an invariant geometry of double field theory
TLDR
A geometrical framework for double field theory in which generalized Riemann and torsion tensors are defined without reference to a particular basis is introduced and it is shown that it contains the conventional Ricci tensor and scalar curvature but not the full Riem Mann tensor.
A symplectic reduction for pseudo-Riemannian manifolds with compatible almost product structures.
We consider a manifold M with a pseudo-Riemannian metric g and an almost product structure P such that g(P (X), P (Y )) = −g(X, Y ). We suppose that the almost product structure P is parallel with…
The geometry of a bi-Lagrangian manifold
The spacetime of double field theory: Review, remarks, and outlook
We review double field theory (DFT) with emphasis on the doubled spacetime and its generalized coordinate transformations, which unify diffeomorphisms and b‐field gauge transformations. We illustrate…
Generalized metric formulation of double field theory
The generalized metric is a T-duality covariant symmetric matrix constructed from the metric and two-form gauge field and arises in generalized geometry. We view it here as a metric on the doubled…
Integrable almost-symplectic Hamiltonian systems
We extend the notion of Liouville integrability, which is peculiar to Hamiltonian systems on symplectic manifolds, to Hamiltonian systems on almost-symplectic manifolds, namely, manifolds equipped…
Branes on Poisson varieties
We first extend the notion of connection in the context of Courant algebroids to obtain a new characterization of generalized Kaehler geometry. We then establish a new notion of isomorphism between…
Manin Triples for Lie Bialgebroids
In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does…
Dirac structures on generalized Riemannian manifolds
We characterize the Dirac structures that are parallel with respect to Gualtieri's canonical connection of a generalized Riemannian metric. On the other hand, we discuss Dirac structures that are…
...
...