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Inverse Scattering and the Geroch Group

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Kleinschmidt,  Axel
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Virmani,  Amitabh
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1211.3044
(Preprint), 339KB

JHEP2013_02_011.pdf
(Any fulltext), 518KB

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Citation

Katsimpouri, D., Kleinschmidt, A., & Virmani, A. (2013). Inverse Scattering and the Geroch Group. Journal of high energy physics: JHEP, 2013(02): 011. doi:10.1007/JHEP02(2013)011.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0010-232A-4
Abstract
We study the integrability of gravity-matter systems in D=2 spatial dimensions with matter related to a symmetric space G/K using the well-known linear systems of Belinski-Zakharov (BZ) and Breitenlohner-Maison (BM). The linear system of BM makes the group structure of the Geroch group manifest and we analyse the relation of this group structure to the inverse scattering method of the BZ approach in general. Concrete solution generating methods are exhibited in the BM approach in the so-called soliton transformation sector where the analysis becomes purely algebraic. As a novel example we construct the Kerr-NUT solution by solving the appropriate purely algebraic Riemann-Hilbert problem in the BM approach.