Differential geometry with a projection: application to double field theory
By Imtak Jeon, Kanghoon Lee, Jeong-Hyuck Park. 2010
234 citations recorded by the source corpus.
In recent development of double field theory, as for the description of the massless sector of closed strings, the spacetime dimension is formally doubled, i.e. from D to D+D, and the T-duality is realized manifestly as a global O(D, D) rotation. In this paper, we conceive a differential geometry characterized by a O(D, D) symmetric projection, as the underlying mathematical structure of double field theory. We introduce a differential operator compatible with the projection, which, contracted with the projection, can be covariantized and may replace the ordinary derivatives in the generalized Lie derivative that generates the gauge symmetry of double field theory. We construct various gauge covariant tensors which include a scalar and a tensor carrying two O(D, D) vector indices.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/e0e191efabcf1b58e3d52fc651875c5100f5c265
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Citations in the corpus
- Supergravity as generalised geometry II: Ed(d) × ℝ+ and M theory (2014, background): “Related “semi-covariant” derivatives, and the corresponding curvature tensors were defined independently by Jeon, Lee and Park in [13, 14].”
- Double Field Theory and N=4 Gauged Supergravity (2011, methodology): “in [13, 14] and couplings to fermions were worked out using this framework [15].”
- Doubled α′-geometry (2013, methodology): “The metric-like approach has been examined in more detail in [24] (in a “semi-covariant” approach that truncates connections) and in [21].”
- Double field theory: a pedagogical review (2013, background): “In [28], the connections were further demanded to live in the kernel of some projectors, allowing for a full determination of the connection.”
- Duality Symmetric String and M-Theory (2013, background): “The part of the connection that is completely determined is given, upon lowering one index with η by [173, 174]”
- β-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework (2013, background): “13) and connection (7)Stringy differential geometry introduced in [41, 42] is a third formalism based on a projection-compatible semi-covariant derivative.”
- Extended geometry and gauged maximal supergravity (2013, background): “More explicit constructions in DFT are presented in [33, 34]–[40].”
- Non‐geometric fluxes in supergravity and double field theory (2012, methodology): “Employing earlier work by Siegel [48, 49], more geometrical formulations of DFT have been further developed in [16,29,52–54].”
- Large gauge transformations in double field theory (2012, background): “Earlier important work can be found in [5–7] and further developments have been discussed in [8–35].”