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  Double field theory, twistors, and integrability in 4-manifolds

Araneda, B. (in preparation). Double field theory, twistors, and integrability in 4-manifolds.

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2106.01094.pdf (Preprint), 795KB
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 Creators:
Araneda, Bernardo1, Author           
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1Geometry and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_3214076              

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Free keywords: High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc,Mathematics, Differential Geometry, math.DG
 Abstract: The search for a geometrical understanding of dualities in string theory, in particular T-duality, has led to the development of modern T-duality covariant frameworks such as Double Field Theory, whose mathematical structure can be understood in terms of generalized geometry and, more recently, para-Hermitian geometry. In this work we apply techniques associated to this doubled geometry to four-dimensional manifolds, and we show that they are particularly well-suited to the analysis of integrability in special spacetimes, especially in connection with Penrose's twistor theory and its applications to general relativity. This shows a close relationship between some of the geometrical structures in the para-Hermitian approach to double field theory and those in algebraically special solutions to the Einstein equations. Particular results include the classification of four-dimensional, possibly complex-valued, (para-)Hermitian structures in different signatures, the Lie and Courant algebroid structures of special spacetimes, and the analysis of deformations of (para-)complex structures. We also discuss a notion of "weighted algebroids" in relation to a natural gauge freedom in the framework. Finally, we analyse the connection with two- and three-dimensional (real and complex) twistor spaces, and how the former can be understood in terms of the latter, in particular in terms of twistor families.

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 Dates: 2021-06-02
 Publication Status: Not specified
 Pages: 62 pages, 2 figures
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 Rev. Type: -
 Identifiers: arXiv: 2106.01094
 Degree: -

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