Inverse scattering and the Geroch group

A bstract 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...

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Published in:The journal of high energy physics Vol. 2013; no. 2; pp. 1 - 29
Main Authors: Katsimpouri, Despoina, Kleinschmidt, Axel, Virmani, Amitabh
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2013
Springer Nature B.V
Subjects:
Algebra
Classical and Quantum Gravitation
Concretes
Construction
Elementary Particles
High energy physics
Inverse scattering
Linear systems
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
Solitons
String Theory
Symmetry
Transformations (mathematics)
Black Holes in String Theory
Global Symmetries
Integrable Field Theories
2D Gravity
ISSN:1029-8479, 1029-8479
Online Access:Get full text
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Summary:A bstract 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.
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP02(2013)011