Stringy differential geometry, beyond Riemann
By Imtak Jeon, Kanghoon Lee, Jeong-Hyuck Park. 2011
251 citations recorded by the source corpus.
While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry that treats the three objects in a unified manner, manifests not only diffeomorphism and one-form gauge symmetry but also $\mathbf{O}(D,D)$ T-duality, and enables us to rewrite the known low energy effective action of them as a single term. Further, we develop a corresponding vielbein formalism and gauge the internal symmetry that is given by a direct product of two local Lorentz groups, $\mathbf{S}\mathbf{O}(1,D\ensuremath{-}1)\ifmmode\times\else\texttimes\fi{}\overline{\mathbf{S}\mathbf{O}}(1,D\ensuremath{-}1)$. We comment that the notion of cosmological constant naturally changes.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/3615f7b16e8c21b2b50ad07f2a826572bd4c20e9
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Citations in the corpus
- On the Riemann tensor in double field theory (2011, methodology): “Many of our results have a direct analogue in the frame formalism of Siegel and some have appeared in [18,19].”
- 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 ”
- 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.”
- Exploring double field theory (2013, methodology): “Here, we construct this action systematically as in [3] closely following the guidelines of [23] (and also [6],[24],[25]): we first introduce connections to covariantize the derivatives under the gauge symmetries of the theory and then impose a set of conditions on them, such as vanishing generalize”
- Doubled α′-geometry (2013, unknown): “27 5.2 Projection to divergence free tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30”
- 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.”
- 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].”
- Extended geometry and gauged maximal supergravity (2013, methodology): “The program to rewrite the theory in a covariant language under O(d, d), the group that includes T-duality, goes under the name of Generalized Geometry [1], or Double Field Theory (DFT) [2] (the latter based on previous constructions on Double Geometry [3]).”
- Supergravity as generalised geometry I: type II theories (2011, background): “The relation to Siegel’s formalism was made in [20] and then expanded on in [22] (see also [23]).”