Frame-like geometry of double field theory

By O. Hohm, S. Kwak. 2010

275 citations recorded by the source corpus.

We relate two formulations of the recently constructed double field theory to a frame-like geometrical formalism developed by Siegel. A self-contained presentation of this formalism is given, including a discussion of the constraints and its solutions, and of the resulting Riemann tensor, Ricci tensor and curvature scalar. This curvature scalar can be used to define an action, and it is shown that this action is equivalent to that of double field theory.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3e8605020cf5e63311e3262f83cf3d1edcbb5369

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Citations in the corpus

Supergravity as generalised geometry II: Ed(d) × ℝ+ and M theory (2014, background): “Such reformulations were first given in the related “doubled” formalism in a series of papers by Hohm, Hull, Kwak and Zweibach [4], building in part on work by Siegel [5].”
On the Riemann tensor in double field theory (2011, background): “The projectors P and P̄ and the generalized metric H can be defined in terms of the frame field as in [7]:”
The spacetime of double field theory: Review, remarks, and outlook (2013, background): “DFT has been applied in various contexts, including the heterotic theory [53], massless and massive type II theories [20,27,54], and their supersymmetric extensions [55–57], and also leads to a compelling generalization of Riemannian geometry [14,44, 58–60], which in turn is closely related to (and ”
Doubled α′-geometry (2013, methodology): “In [20] this formalism has been related to the double field theory actions of [18, 19] and to a metriclike formulation.”
β-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework (2013, background): “An analogous DFT formalism with similar objects was developed before in [43], and its relation to [23] has been established in [34], that is also helpful here.”
Differential geometry with a projection: application to double field theory (2010, methodology): “Note added: after submitting the first version of this manuscript to arXiv, a related interesting work by Hohm and Kwak appeared [ 36 ].”
The effective action of double field theory (2011, methodology): “5), where the label a is replaced by A and the standard Lie bracket is replaced by the Cbracket [38] (see [49] for a discussion of torsion in the context of Generalized Geometry).”
Spheres, Generalised Parallelisability and Consistent Truncations (2014, methodology): “In the original formulation [13, 14] E ≃ TM⊕T M , and the structure on E, together with the natural analogue of the Levi–Civita connection, capture the NSNS degrees of freedom of type II theories and the bosonic and fermionic equations of motion [15] (see [16] and also [17] for earlier geometric ref”
The local symmetries of M-theory and their formulation in generalised geometry (2011, unknown): “Recent, related work include the extension of double field theory to Heterotic string theory [32] and type II strings [33–35] and other interesting studies given in [36–46].”
Extended geometry and gauged maximal supergravity (2013, methodology): “20) (the procedure is similar to the frame-like formalism of the DFT given in [30]), and consider diffeomorphisms that close under the twisted constraints of Section 3.”
Double field theory: a pedagogical review (2013, methodology): “This frame formulation was introduced in [2], later related to other formulations in [18], and also discussed in [68].”
Supergravity as generalised geometry I: type II theories (2011, background): “Furthermore, comparing with [14, 15, 22] we see that locally these are the same tensors that have appeared in Siegel’s formulation.”
Exploring double field theory (2013, methodology): “3 Geometry, connections and curvature It was shown in [3],[6],[23]−[25] that the action and equations of motion of DFT can be obtained from traces and projections of a generalized Riemann tensor.”
Double field theory of type II strings (2011, background): “(See [19, 20] for earlier work by Siegel and [21–37] for related papers.”