Solitons, infinite symmetries and integrable field theories

Abstract

This project aims the study of integrable field theories, infinite dimensional algebras and soliton theory with the objective of developing methods in non-linear phenomena and non-perturbative aspects of field theories. The project is the natural continuation of the work being developed by the group in the past few years on those topics and will be implemented following two main directions. The first concerns the structure of integrable hierarchies in $1+1$ dimensions, the systematic construction of soliton solutions in terms of representation theory of Kac-Moody algebras, symmetries and its generalization to supersymmetric integrable hierarchies. The second concerns the extension of the known technology employed in constructing conserved charges and solutions in two dimensional models to theories in dimensions other than two. This is a highly nontrivial problem which may reveal new symmetries and algebraic structures important for the understanding of many non-perturbative aspects of field theories in $3+1$ dimensions. (AU)