Objective
There is a remarkable similarity between the mathematics of these two apparently disparate fields. Approaches to these special field theories and also to special solutions of field theories in three or more dimensions of space-time, have led to the discovery of new structures in mathematics (a variety of infinite-dimensional algebras and the notion of quantum groups), and to a plethora of as yet not properly explained phenomena discovered more or less empirically, sometimes in the course of numerical integration of the non-linear equations. The whole question of quantum integrability remains obscure, despite the discovery of many explicit examples such as the sigma models or Toda theories.
Recent advances in string theory have led to renewed interest in the widespread phenomenon of weak-strong coupling duality, observed in many integrable systems, and special classical solutions such as monopoles and instantons.
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.
In the framework of the project the following work will be done: new solutions will be sought to Einstein's equation in general relativity; the applications of infinite algebras to gauge theory and integrable field theory will be investigated; topics in integrable classical and quantum field theory will be studied; four-dimensional integrable field theories, supergravity, twistor reformulations of string theory, W-strings and integrable hierarchies will be studied; extensions of string theory will be investigated; integrable non-linear wave equations and special solutions to non-linear wave equations will be studied; work on the application of certain integrable models in low temperature condensed matter systems will be carried out; and various applications of integrable field theory in statistical systems will be developed.
Topic(s)
Call for proposal
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DH1 3LE DURHAM
United Kingdom