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Verwertbare Ergebnisse
The objective of the research project is to enhance the existing knowledge of classical solutions both in classical general relativity and string-modified gravity using solution-generating methods based on hidden symmetries and integrability properties. It includes both development of mathematical methods and study of physical implications and aims to clarify some basic problems of general relativity within the context of the string theory.
The scientific work of the team members has included progress on the following topics: the development of new algebraic methods for computing exact correlation functions in quantum integrable field theories; the study of integrable lattice models including the discovery of exactly solvable three-dimensional models; development of the Bethe ansatz techniques and their application to the solution of Knizhnik-Zamolodchikov equations; establishing explicit connections between integrable systems and low-energy limits of supersymmetric field theories; the explicit construction of singular vectors and the representation theory of conformal algebras; new results concerning the Calogero-Moser model and Toda chains; the conceptual bais of classical integrability and its relationship with mathematical structures, Lie algebras and differential geometry; the twistor approach to the formulation of string theory and the theory of membranes; the uses of symmetry, explicit and hidden, for solving nonlinear wave equations; the low energy limit of heterotic string theories; the dynamics of colliding plane waves in general relativity and new techniques for solving Einstein's calculations; skyrmion scattering; the relationship between threshold, or near-threshold multi-particle amplitudes and integrable systems; the quantum Liouville model; properties of special functions arising in the study of quantum integrable systems and in the calculation of their correlation functions.
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